This is an appeal from a court-tried case in which the circuit court found against the plaintiffs on each of three counts, Count I being for malicious prosecution, Count II being for slander, and Count III being for false arrest. The facts underlying these counts occurred over a period of several years and apparently evolved from marital difficulties between plaintiff Joseph Hoog and his former wife, Carol Strauss Hoog, daughter of the defendants.
On January 14,1971, Carol Hoog had her father’s car parked in front of her husband’s brother’s house and Joseph Hoog’s car was parked directly in front of the Strauss car. As a result of a fight between husband and wife, the front end of the Strauss car was damaged, Joseph alleging his wife drove her father’s car into his car and Carol alleging her husband backed up into the car belonging to her father. After seeing the damages to his car and being told by his daughter what had happened, the defendant Stanley Strauss swore out a complaint against Joseph for malicious destruction of property. Joseph was convicted of this charge in municipal court and then appealed. While the appeal was still pending, the city prosecutor and Joseph and his attorney agreed that the case would be dismissed if Joseph paid the court costs. It is this case whose prosecution forms the basis of the malicious prosecution charge.
On March 15, 1974, the plaintiff Shelley Hoog, Joseph’s wife, was seen by a police officer sitting alone in a pickup truck late at night in front of the Strauss home. She told the officer she had just had an argument with her husband Joseph and had left him at home so she could be alone to think. Then the officer heard the sound of breaking glass and believing a burglary was in progress, he arrested Shelley Hoog. Just then Joseph ran from the defendants’ house toward the truck and was also arrested. The police woke up the defendants, told them what had happened and that the glass on one of their doors was broken, and asked if they wished to prosecute. The defendants said they did. In contrast to this, the plaintiffs presented evidence that Shelley Hoog had not yet been arrested and that when aroused by the police, the defendants demanded her arrest. All charges against Shelley were later dropped. This is the basis of the false arrest count.
Subsequently, various proceedings were held on some of the charges filed against Joseph in connection with this incident. He eventually pleaded guilty to charges of public drunkenness and destruction of private property and was given a suspended sentence. This occurred on January 23, 1975. Right after the trial Joseph and his attorney met with the defendants and the city *356prosecutor and he agreed to pay for the damaged glass door. The plaintiffs presented testimony from the prosecutor and themselves that after this agreement had been made the defendants publicly accused the plaintiff Joseph Hoog of having fire bombed their car. The defendants presented testimony from the police officer who had arrested the plaintiffs and who was present during and after the trial that he had heard nothing about fire bombing at all. They also testified on their own behalf that the defendant Stanley Strauss had merely said to Joseph’s attorney, “Will you please tell your client not to fire-bomb my car.” These remarks, whatever they consisted of, form the basis of the slander count.
The trial judge found against the plaintiffs on all three of their counts. He said they had not met their burden of proof on the malicious prosecution charge or the false arrest charge. As to the slander charge, he said it failed for lack of any proof as to damages. The plaintiffs contend as to the malicious prosecution and false arrest charges that the judge’s findings are not supported by the evidence. They contend that as to the slander charge, the judge’s findings are against the overwhelming weight of the evidence. They also contend that they did not need to prove damages because defendant’s remarks constituted slander per se. Finally, they assert that they were erroneously prevented from cross-examining the defendants’ witnesses as to matters affecting their credibility.
The standard of review in a court-tried case has been set out in numerous cases so it need not be reviewed in detail here. The standard is set out and discussed in Rule 73.01 and Murphy v. Carron, 536 S.W.2d 30, 32[1, 2] (Mo.banc 1976). Under it, we will examine the contentions that as to the malicious prosecution and false arrest charges, the trial court’s findings have no substantial evidence to support them.
Both of the defendants and the arresting police officer testified that defendants had not asked Shelley Hoog be arrested; that they merely said, upon being asked, they wished to prosecute the Hoogs for destroying their property. The police officer testified he had arrested Shelley Hoog when he heard the glass break, before the defendants had even been contacted by the police. Certainly this constitutes substantial supporting evidence of a finding that the defendants in no way caused the arrest of Shelley. She was already under arrest before they spoke to the police. It is the rule in this state there is no case of false arrest made out unless the plaintiff proves the defendant was the cause of the arrest. Wehrman v. Liberty Petroleum Company, 382 S.W.2d 56, 60[3] (Mo.App.1964). Plaintiffs here did not prove that the defendants caused Shelley’s arrest. The trial court’s judgment against the plaintiffs on Count III, the false arrest charge, was supported by substantial evidence.
With respect to the malicious prosecution charge, no case is made unless the plaintiff proves that the proceedings against the plaintiff, here the prosecution for destroying the defendants’ car, terminated in his favor and unless he shows lack of probable cause for such proceedings. Palermo v. Cottom, 525 S.W.2d 758, 763[5] (Mo.App.1975). We have failed to find any decision in this state holding the ending of a prosecution by a dismissal of the charges brought about by a compromise agreed to by the person being prosecuted, as happened here when Joseph Hoog agreed to pay court costs in return for a dismissal of the charges against him, on his appeal, constitutes a termination of the proceedings in the plaintiff’s favor for purposes of a malicious prosecution suit. Cf., Cooper v. Associated Laundries, 83 S.W.2d 591, 592-93 (Mo.App.1935). A conviction in a lower court, however, on the charge brought against a plaintiff in a malicious prosecution suit constitutes prima facie evidence of probable cause for the prosecution even though the case is dismissed after appeal to the circuit court. Plaintiff then has the burden of proving the conviction was based on false or fraudulent testimony by the defendants. La Chance v. National Pig*357meats & Chemical Co., 104 S.W.2d 693, 699[9] (Mo.App.1937).
Here, both the former Carol Hoog and the defendant Stanley Strauss testified that Carol had told her father Stanley that the plaintiff Joseph had backed his car into the defendants’ car. They also testified that she had told him that Joseph had twisted the ignition in the Strauss car and broken it. In addition, Carol testified that she had seen Joseph do this damage and Stanley testified he had himself seen the car, damaged just to the extent Carol had said it was, before he filed a complaint against Joseph. This is substantial evidence to support a finding that the defendant did not give false or fraudulent testimony against Joseph at the latter’s trial. Because this was necessary for the plaintiffs to prove and they did not do so, the judgment against them on Count I, the malicious prosecution charge, was supported by substantial evidence.
We turn now to the slander charge. We cannot agree that the trial court’s judgment on this count was against the overwhelming weight of the evidence. The plaintiffs testified that the defendant Stanley Strauss directly accused Joseph of fire bombing the Strauss car. The city prosecutor’s testimony corroborated theirs. The defendants, however, testified that no such accusation was made but rather Stanley had asked Joseph’s attorney to tell Joseph not to fire bomb the Strauss car. In addition, a police officer said he heard no remarks about fire bombing despite the plaintiffs’ claim that such remarks were carried over loudspeakers to the entire courtroom. We defer to the court’s finding because it is based on substantial evidence.
Assuming such a valid finding, the question then becomes: Does this remark constitute slander per se, eliminating the need for a showing of damages? Because the trial court found that there was no showing of damages (plaintiffs do not claim they made such a showing) and therefore the slander charge failed, it obviously held that Strauss’ remark, “Will you please tell your client not to fire-bomb my car,” was not slander per se. We agree. Accusation of a crime is slander per se and such an accusation need not be direct, but if it is not direct, it must be the only inference that could be reasonably drawn from the language used. Walker v. Kansas City Star Company, 406 S.W.2d 44, 50-51[1, 2] (Mo.1966); Priest v. Central States Fire Ins. Co., 223 Mo.App. 122, 9 S.W.2d 543, 544[7] (1928). Here, other inferences could be drawn besides that Joseph Hoog had fire bombed or threatened to fire bomb a car. For example, it could be inferred that Strauss thought Hoog was the kind of person who would fire bomb his car but this does not mean he actually ever committed the crime. The defendant’s statement, therefore, was not slanderous per se, and to support their slander charge the plaintiffs would have had to show damages, which they did not. We affirm the trial court’s finding against the plaintiffs on Count II.
Plaintiffs also contend the trial court erred in not allowing them to ask defendants’ witnesses several questions on cross-examination. In this category are several specific rulings about which plaintiffs complain. Most of these rulings concern questions which plaintiffs now claim they should have been allowed to ask because the answers would show bias or prejudice and affect the credibility of the witness. “Proof of a witness’s or party’s bias or prejudice in favor of or against any of the parties to an action may properly be shown and considered as bearing upon the credit which should be accorded the testimony of a witness . . . When bias or prejudice is being explored, broad discretion is vested in the trial court as to the extent of the cross examination.” Vosevich v. Doro, Ltd., 536 S.W.2d 752, 760[11, 12] (Mo.App.1976). See also, Thornton v. Vonallmon, 456 S.W.2d 795, 798[1—4] (Mo.App.1970).
Plaintiffs’ first contention of error under this point concerns two questions asked of Carol Stitt. On direct examination she testified only that she was the daughter of Stanley Strauss, that she was formerly married to Joseph Hoog, that Hoog had backed his car into her father’s car and had twisted and broken the ignition *358of her father’s car and that this is what she had told her father that Hoog had done. On cross-examination plaintiffs brought out that “at this particular time” Carol was still married to Joe. Then objections were sustained, apparently on the basis of irrelevancy, to the question, “And how long did you have difficulties with Joe?” and the question, “How long had you and Joe been separated?” When the trial court said it failed to see the relevancy of the questions, plaintiffs’ lawyer said “it shows that there was hard feelings between the two of them at the particular time and that it was not something that — an incident just of this particular minute” (emphasis added). From this statement and plaintiffs’ brief it is clear that plaintiffs were not claiming Carol was giving false testimony at trial but that she had lied to her father when she told him how his car had been damaged. Plaintiffs’ theory was that Carol, not plaintiff, was responsible for the damage to the car. Carol was not a defendant in the case and only her father was being sued under Count I for malicious prosecution arising out of this incident. Showing that Carol had hard feelings toward or bias against plaintiff would not be relevant where plaintiffs were not trying to show that her trial testimony with regard to what she had told her father was false. Her feelings toward plaintiff are irrelevant on this issue because even if she had lied to her father this would not show that he did not or could not have had a good faith belief that plaintiff had committed a criminal act. Probable cause, in a malicious prosecution case, depends not on the actual facts but on defendants’ honest and reasonable belief in the guilt of the accused. Dodson v. MFA Insurance Co., 509 S.W.2d 461, 467[1] (Mo.1974); 52 Am. Jur.2d, Malicious Prosecution § 72, pp. 232-33; 54 C.J.S. Malicious Prosecution § 20, p. 977. Attempting to show that the actual facts were other than defendant had been told they were is thus irrelevant. The trial court did not err in sustaining the objections to these questions.
Plaintiffs’ second subpoint in this category concerns the trial court’s action in sustaining an objection to a question asked of Carol as follows: “What was the purpose of coming to this location?” On appeal plaintiff asserts that this question was relevant “in determining what actually occurred.” As noted above, what actually occurred is not relevant.
In plaintiffs’ next subpoint they contend the trial court erred in sustaining an objection to this question asked of Carol: “At the time were you under a doctor’s care?” At trial plaintiffs did not attempt to show the relevancy of this question. On appeal they contend it was relevant “in determining what actually occurred.” Again, this is not relevant. Plaintiffs also argue that this inquiry was relevant in determining whether her father was entitled to rely on her statements. The reasonableness of his belief that plaintiff had committed a crime is relevant but this question does not go to the reasonableness of his belief. The court did not err in sustaining the objection to this question.
Plaintiffs’ fourth subpoint concerns the court’s action in sustaining an objection to this question asked of defendant Stanley Strauss: “Mr. Strauss, at that particular time was your daughter Carol under a doctor’s care?” After the court sustained an objection that the question was irrelevant, plaintiffs made “an offer of proof that if this witness were permitted to testify he would'testify that she was under a doctor’s care, to-wit: a psychiatrist, that she was taking medication as prescribed by the doctor at that particular time.” On appeal plaintiffs argue only that this question was relevant because the “information would indicate that Carol Stitt had given false testimony” in that she had earlier answered, “No, sir, I had not” to the question, “Had you had any marijuana, narcotics, or other drugs that you were taking that particular night?” Assuming this suggested response would be what the witness would have said and that this would be a contradiction of her testimony, it is still unclear how this would aid plaintiffs’ case in that plaintiffs do not contend Carol said anything to her father other than what she had testified to. Apparently plaintiffs seek to show that Carol lied to her father about the true facts of the occurrence but as discussed above, this is not relevant. (Plaintiffs did *359not argue at trial and do not argue now that this question and answer would be relevant to indicate that defendant Stanley’s belief in the veracity of what his daughter told him was not reasonable and we do not consider its relevancy on this ground.)
Plaintiffs’ fifth and seventh sub-points are very similar. Plaintiff attempted to ask defendant Stanley Strauss, “Were you in favor of this marriage [between his daughter and plaintiff] to begin with?” The trial court sustained an objection to the question on the grounds of irrelevancy. The court also sustained a like objection to the following question asked of defendant Betty Strauss: “Isn't it a fact when your daughter married Joe you didn’t approve of it?” Assuming that the witness would have said they were against the marriage between their daughter and plaintiff when they got married, that this was because they did not like plaintiff then and that this would show they did not like him either when they pressed charges against him or when they were testifying in the instant case, the questions were proper as tending to show bias and prejudice against plaintiff. However, it was already abundantly clear - from all the evidence in the case that there was disaffection, animosity and ill feeling between defendants and plaintiff. Under these circumstances it was within the trial court’s discretion to limit questioning as to specific instances and examples of the par- ■ ties’ bad feelings particularly when the two questions about which plaintiffs complain are only remotely relevant in proving bias against plaintiff at some relevant time. State v. Glass, 554 S.W.2d 426, 429-31[4-6] (Mo.App.1977). Although it is not within the trial court’s discretion to prevent cross-examination on bias and prejudice entirely, Thornton v. Vonallmon, 456 S.W.2d 795, 798[4] (Mo.App.1970), here the trial court did allow several questions on cross-examination of these two witnesses regarding their bias and prejudice against plaintiff. The point is without merit. State v. Campbell, 543 S.W.2d 508, 511-12[8-9] (Mo.App.1976).
Plaintiffs’ final (sixth) subpoint, which has no relation to the other sub-points, concerns the court’s action in overruling an objection to an answer given by the city attorney who handled the prosecution of plaintiff on the charge of destruction of property (defendant’s car). The witness was asked if there was an agreement to dismiss the case if plaintiff would pay court costs. The witness said there was such an agreement. He then started to explain why he would not simply nolle prosse the case. Plaintiff objected that the answer was going beyond the scope of the question. Even though the answer did go beyond the scope of the question, we find no reversible error in overruling plaintiffs’ objection and allowing the testimony in because, as previously set forth, there is sufficient competent evidence in this court-tried case to support the trial court’s decree. Broyles v. Broyles, 555 S.W.2d 696, 700[10] (Mo.App.1977). In Broyles the court notes that in a court-tried case it is practically impossible to predicate reversible error on the erroneous admission of evidence.
The trial court’s judgment against the plaintiffs on all three counts is affirmed.
DOWD and KELLY, JJ., concur.