We granted certiorari to review the court of appeals’ affirmance of the trial court’s bench ruling that Cathy S. Parker’s claim against Harry D. Irizarry for pregnancy and confinement expenses and reimbursement of child-rearing expenses from April 15, 1985, to May 30, 1989, is barred by the doctrine of equitable estoppel. State Dep’t of Human Servs. ex rel. Parker v. Irizarry, 893 P.2d 1107, 1110 (Ct.App.), cert, granted, 910 P.2d 425 (Utah 1995). The court of appeals ruled that the trial court acted within its discretion in applying the doctrine of equitable estoppel to a situation where a parent made a claim for reimbursement of child-rearing expenses, and upheld the trial court’s conclusion that the requirements of equitable estoppel had been satisfied. Id.
STANDARD OF REVIEW
Before enumerating the facts, we address the standard of review. An appellate court “will not reverse the findings of fact of a trial court sitting without a jury unless they are ‘against the clear weight of the evidence,’ thus making them ‘clearly erroneous.’ ” MacKay v. Hardy, 896 P.2d 626, 629 (Utah 1995) (quoting In re Estate of Bartell, 776 P.2d 885, 886 (Utah 1989) (additional internal quotation omitted)). In this case, the parties do not challenge the trial court’s factual findings, and the court of appeals accepted them as correct. An appellate court reviews the trial court’s conclusions of law for correctness. Newspaper Agency Corp. v. Utah State Tax Comm’n, 938 P.2d 266 (Utah 1997); State v. Christensen, 866 P.2d 533, 535 (Utah 1993).
The issue of whether equitable estop-pel has been proven is a classic mixed question of fact and law. As we observed in State v. Pena, 869 P.2d 932 (Utah 1994), we give trial court determinations of such mixed questions differing degrees of deference, depending on several considerations. The doctrine of equitable estoppel is simply stated, yet it is applicable to a wide variety of factual and' legal situations. The variety of fact-intensive circumstances involved weighs heavily against lightly substituting our judgment for that of the trial court. Id. at 939. Therefore, we properly grant the trial court’s decision a fair degree of deference when we review the mixed question of whether the requirements of the law of estoppel have been satisfied in any given factual situation.
FACTS
At the outset, we briefly recite the trial court’s uncontested findings of fact. Parker and Irizarry began a relationship in June of 1984 which led to Parker’s pregnancy, discovered in July or August of 1984. When Iri-zarry .visited Parker in California, where she had moved in July, she informed him of her pregnancy and of her belief that he was the father. He responded by offering his support to her. After returning to Utah, he telephoned and wrote to her several times. Parker apparently did not attempt to contact Irizarry during this time. On at least three occasions, once in September of 1984, once in November of 1984, and once in January of 1985, he telephoned her in California, during which conversations she told him that she did not want any money, was able to take care of herself, wanted nothing to do with him, and intended to name her offspring “Parker.” In November of 1984, Irizarry sent a letter to Parker in which he thanked her for accepting approximately twenty dollars from him. There appears to have been no further contact between the parties until June of 1985 when Parker telephoned Irizarry and left a message with his roommate that she had delivered twins in April of 1985 and that she had named them “Parker.”
*679Irizarry married his current wife in October of 1985, started a family, and moved to Puerto Rico. Parker hired a detective to locate him in February of 1987. These efforts were unsuccessful, and he had no notice that she was looking for him. Parker’s mother wrote a letter to a friend of Irizarry’s in August of 1987 containing a message for Irizarry that concluded with the statement, “We are not concerned about taking him to court_ His court will come later — he cannot say that they are not his children there.” The trial court found that Irizarry received the letter when he returned to Salt Lake in September of 1987 and that Parker was apparently unaware of this letter and its contents. After seeing Irizarry in. the Salt Lake City Airport, Parker filed her complaint in this action on May 30,1989.
The trial court ruled that on these facts there was sufficient evidence to establish the elements of equitable estoppel.1 Parker argues that estoppel should not apply because (1) a right to reimbursement that has not yet come into being cannot be waived in advance, (2) the right to child support should be independent of the personal relationship between the biological parents, and (3) an unwed father subject to the delayed filing of a paternity action is adequately protected by Utah Code Ann. § 78-45a-3, which provides, “The father’s liabilities for past education and necessary support are limited to a period of four years next preceding the commencement of an action.” We will address Parker’s arguments as we examine the relationship between child support, reimbursement for child-rearing expenses, and the doctrine of equitable estoppel.
ANALYSIS
A. Distinction Between “Child Support” and “Reimbursement”
We begin by noting that no statement of rejection on Parker’s part, no matter how strong, could have legally defeated the children’s right to support. Utah’s child support laws and the guidelines that accompany them are designed to maximize support to children from both of their parents. See Utah Code Ann. § 78^5-3(1) (1996) (“Every father shall support his child ....”); id. § 78-45-4(1) (“Every woman shall support her child_”). We emphasized in Hills v. Hills, 638 P.2d 516, 517 (Utah 1981), that the right of minor children to support cannot be “bartered away, extinguished, estopped or in any way defeated by the agreement or conduct of the parents.” (Citing Gulley v. Gulley, 570 P.2d 127 (Utah 1977).) It is well established that “[ejvery parent has the duty to support the children he has brought into the world,” and this duty is inalienable. Gulley, 570 P.2d at 128-29. “Moreover, the minor children who are the beneficiaries of this duty [and] not parties to [an agreement relinquishing support] ... [cannot] be bound thereby.” Id. at 129. Therefore, “the just and logical consequence of the duty of parents to support their children is that if they are left in need and a third party provides them necessities, he is subrogated to the child’s right and may obtain reimbursement therefor.” Id. (emphasis added) (footnote omitted).
In the instant case, however, the issue on appeal is whether the trial court abused its discretion in applying equitable estoppel to bar Barker’s claim for reimbursement of child-rearing expenses she has paid. This is not an action for “past due child support,” as Parker incorrectly represents. This is an action for reimbursement to a parent, not a third party, of monies already expended in support of children who by Parker’s own admission were well cared for and not left .in ■ need. She testified specifically that the twins had never gone without food, clothing, or shelter. In Wasescha v. Wasescha, 548 *680P.2d 895 (Utah 1976), a mother seeking retroactive payments claimed, much as Parker does here, that her action was not for reimbursement because all sums recovered would be placed in trust for the children. This court rejected that reasoning and applied estoppel, stating that “there seems to be an admission that the children’s right to support amply was supplied ..., which would eliminate their need for support or, if you please, double support.” Id. at 896.
We clearly distinguished between actual child support and reimbursement in Larsen v. Larsen, 5 Utah 2d 224, 227, 300 P.2d 596, 598 (Utah 1956), stating:
[Bjecause the state is interested in the child’s welfare the parents cannot effectively release future payments of support money by agreeing with the other to that effect. However, this does not mean that a mother may not by her actions or representations, or both, preclude herself from recovering past due installments of support money to reimburse her for the money which she has spent for the support of the child.
Thus, once paternity is legally established, a biological mother cannot disclaim future child support on behalf of her children. Before the father is legally identified, however, he has no legal obligation to the child, and it only stands to reason that a payment cannot become “past due” until it initially becomes due. Consequently, although section 78-45a-3 recognizes a claim to retroactive payment for the four years preceding the filing of the suit, such payments are “reimbursement” rather than “child support.”
This conceptual separation of “reimbursement” and “child support” recognizes the hard realities. Genuine child support must be available to meet the current needs of the child, and payments made later cannot alter the level of support that the children have already received. Understanding this, we decline to employ the euphemism “back child support” for payments that were not available to meet past needs and are not even legally required to be used for the children’s present and future needs. See Larsen, 300 P.2d at 598. Only “reimbursement” accurately describes such payments.
Parker actively repudiated the establishment of a child support obligation, without which a right to reimbursement has no foundation, and she gave Irizarry abundant notice of that repudiation. Under orn-ease law, the right to reimbursement is subject to legal and equitable defenses in the same manner as any other debt. Baggs v. Anderson, 528 P.2d 141,143 (Utah 1974). As the court of appeals correctly observed, an appellate court “will not overturn the trial court’s application of equitable estoppel absent an abuse of discretion.” Irizarry, 893 P.2d at 1108-09; see Utah State Dep’t of Social Servs. ex rel. Borland v. Chandler, 733 P.2d 144 (Utah 1987) (holding that lach-es, an equitable defense, could be asserted by defendant in paternity action).
B. Application of Estoppel
The elements essential to invoke the doctrine of equitable estoppel are:
(1) an admission, statement or act inconsistent with the claim afterwards asserted,
(2) action by the other party on the faith of such admission, statement or act, and
(3) injury to such other party resulting from allowing the first party to contradict or repudiate such admission, statement or act.
Celebrity Club, Inc. v. Utah Liquor Control Comm’n, 602 P.2d 689, 694 (Utah 1979). The trial court found that (1) Parker made no calls and wrote no letters to Irizarry asking for support; (2) she left Irizarry’s name off the children’s birth certificates; (3) she had the support and financial assistance of her family, and her family discouraged her relationship with Irizarry; and (4) Irizarry was willing to support the children, but Parker refused support. In view of these findings, the trial court concluded that Parker *681Although the trial court’s findings are not uncontroverted, neither are they wholly lack- ■ ing evidential support. Therefore, our only task is to determine whether the trial court correctly applied the law to the facts in arriving at its conclusion that estoppel applies.
*680made statements, took actions that led [Iri-zarry] to reasonably conclude that [Parker] wanted nothing to do with him and didn’t want his support. In reliance on that, [Irizarry] got on with his life, got married and started a family and under those circumstances should not be responsible for the payment of support, until ... this complaint was filed.
*681Parker contends that a child support obligation should be independent of the personal relationship between the biological parents. We agree. However, she fails to recognize the distinction between a personal and a legal relationship and between a relationship with the child and one with the mother. While the support obligation must be independent of the father’s personal relationship with the mother, it cannot be independent of his legal relationship to the child. Parker’s statements that she wanted nothing to do with Irizarry or his money might possibly be interpreted as rejecting only a personal relationship with him. However, when she went further and made a point of informing him that she was naming the twins Parker, omitted his name from their birth certificate, and refused his offer of support, she strongly indicated she did not want him to have any relationship with the twins. Additionally, the trial court found, regarding the letter from Parker’s mother, that although “[t]here is nothing authorizing the mother to take [the] position [that the Parkers would not seek support], ... the letter being received by [Irizarry] would strengthen his reliance and his position, or his belief that nobody was looking to him for support for these children.”
We agree with the court of appeals that Parker’s plainly worded rejections2 of Irizarry’s offers of support made directly to him, not through a third party,3 plus her actions taken after the twins’ births constituted statements inconsistent with her later asserted claim for child support. Irizarry, 893 P.2d at 1109, 1110. Therefore, the first element of estoppel is satisfied.
The second element of estoppel requires that Irizarry reasonably changed his position in reliance upon Parker’s representations. This is a largely factual question and perilously fraught with uncertainty. Irizarry married, and he and his wife have four children. He testified that he began dating his current wife only after he became convinced that Parker wanted no contact and would accept no financial help from him. He reasonably knew that she was capable of providing for the children. He further testified that he has a low-paying job as a first lieutenant in the United States Marine Corps and virtually no savings. The- trial court found that “in reliance on [Parker’s statements] he got on with his life, got married and started a family.” Certainly the awareness of a consistent and long-term financial drain such as child support would logically have affected critical life decisions such as family size, pursuit of higher education, type of job, and acceptable salary level. In addition, if the support obligation had been established earlier and Irizarry had been making current payments throughout the years, his position would be different now in that he would not be potentially faced with “double” payment for both current support and reimbursement.
A situation such as this, which presents this court with a close question on the facts, illustrates the wisdom of our “fair degree of deference” to the trial court. While the evidence before the trial court was somewhat ambiguous, “ ‘the trial judge has observed “facts” such as the witness’s appearance and demeanor, relevant to the application of the law that cannot be adequately reflected in the record available to appellate *682courts.’ ” Jouflas v. Fox Television Stations, Inc., 927 P.2d 170, 174 (Utah 1996) (quoting C & Y Corp. v. General Biometrics, Inc., 896 P.2d 47, 53 (Utah Ct.App.1985)); see also Pena, 869 P.2d at 939. Therefore, while in reviewing a mixed finding of fact and law appellate “ ‘courts are free, to make an independent determination of the trial court’s conclusions,’ ... the trial court’s factual findings shall not be set aside on appeal unless clearly erroneous.” State v. Tyler, 850 P.2d 1250, 1253 (Utah 1993) (quoting State v. Templin, 805 P.2d 182,186 (Utah 1990)). To meet the clearly erroneous standard, an appellate court must determine that the trial court’s factual findings are “against the clear weight of evidence,” or the court must “otherwise reach[ ] a definite and firm conviction that a mistake has been made.” State v. Walker, 743 P.2d 191, 193 (Utah 1987). After full review of the evidence, there is no basis for our having a definite and firm conviction that the trial court was mistaken in finding that Irizarry changed his position in reasonable reliance upon Parker’s representations. Therefore, the second element of estoppel is satisfied.
Turning to the injury element of estoppel, the facts of the case before us rebut Parker’s argument that section 78-45a-3’s four-year cap on recovery of reimbursement renders estoppel unnecessary by always providing adequate protection for an unwed father. Although $10,000 — the amount at issue here — may not be a large amount by some standards, it looms large to someone whose cash assets total less than $200 and who owns nothing substantial that he could sell. Irizarry and his wife have four children of their own who have a claim to support at least as strong as that of the twins. As it is, Irizarry is required to pay a monthly ongoing support obligation for the twins, which he does not contest. If estoppel were not available, then the later-born children of a father such as Irizarry could be deprived of their actual present support in order to reimburse the mother of earlier-born children for her past support of those children even though there is no legal requirement that such payments be used for the benefit of the children.
Furthermore, according to the income statements for the relevant period, upon which plaintiff Department relied for its support guidelines, Parker earned more than $105,000 from 1986 through 1991, while Iri-zarry’s total.income from 1985 through 1990 was only slightly more than $72,700. During much of this period, Parker was living with her parents and her mother was providing child care. Parker contributed to the household expenses and paid her mother for watching the children when she could. Her parents paid her medical expenses, largely through their insurance, and she is gradually endeavoring to pay them back. Thus, it would appear that Parker’s children may have had access to a standard of living well beyond that available to Irizarry’s later-born children. Therefore, we decline to overrule case law that permits the application of es-toppel to reimbursement for child-rearing expenses.
CONCLUSION
The trial court correctly applied es-toppel, and the court of appeals properly affirmed the trial court. Any inclination on our part to decide differently is insufficient justification for overturning the fact-based conclusions of two lower courts. This is especially so since “[c]onsistent with- [this] [c]ourt’s standard of review on the issue of waiver,” an appellate court grants “similar broadened discretion to the trial court on the issue of equitable estoppel.” Trolley Square Assocs. v. Nielson, 886 P.2d 61, 65 (Utah Ct.App.1994) (citing Soter’s, Inc. v. Deseret Fed. Sav. & Loan Ass’n, 857 P.2d 935 (Utah 1993)). ‘
Affirmed.
STEWART, Associate C.J., and RUSSON, J., concur in Justice HOWE’s opinion.. The trial court did not specifically mention equitable estoppel in its findings of fact and conclusions of law. Rather than choosing between the parties' conflicting draft findings and conclusions, on March 8, 1993, the trial judge entered a handwritten note on the transcript of his February 11, 1993, bench ruling, adopting the ruling as his findings of fact and conclusions of law. That bench ruling did not specifically mention "equitable estoppel,” but the ruling makes reference to the three elements of estop-pel, namely, statements by Parker adverse to her later claim, reasonable reliance by Irizarry on those statements, and detriment to Irizarry should Parker be allowed to repudiate her prior statements. Thus, we treat this bench ruling as the trial court's judgment that the facts in this case support a finding of equitable estoppel.
. " ‘It is not enough that the person who heard [the representations] deemed that he was warranted in acting as he did; the language used ought of itself to furnish the warrant.' " Farmers & Merchants Bank v. Universal C.I.T. Credit Corp., 4 Utah 2d 155, 159, 289 P.2d 1045 (1955) (quoting J.T. Fargason Co. v. Furst, 287 F. 306, 310 (8th Cir.1923)).
. See Burrow v. Vrontikis, 788 P.2d 1046, 1048 (Utah Ct.App.1990), in which the court found that a biological father’s failure to pay child support was based on more than mere silence when the mother of the child told a friend' that she did not ever want to see the child's biological father again and the friend relayed the statement to the father, although the mother had not directed her to. For a more complete discussion, see the court of appeals' analysis in State v. Irizarry, 893 P.2d 1107 (Utah Ct.App.1995).