Aubrey Moncrief, an employee of Alabama Power Company, was involved in a shooting incident with the police of Oxford, Alabama, as a result of which he was suspended from his employment. Local Union 391, International Brotherhood of Electrical Workers, of which Moncrief was a member, filed a grievance objecting to Moncrief’s suspension. The collective bargaining agreement provided a three-stage grievance procedure culminating in binding arbitration. The Company denied the grievance at each stage, and the Union finally requested arbitration of the grievance.
After the request for arbitration but before the arbitration had commenced, the Grand Jury indicted Moncrief, whereupon the Company “converted” his suspension into a discharge. Shortly thereafter Union and Company officials met to discuss the grievance of another employee. The Union contends that at that meeting the Company waived the necessity for filing a separate grievance for his discharge; the Company asserts that no such waiver was made, or that if it was made, it was ineffective.
The grievance then proceeded to arbitration. The Company sought to submit to the arbitrator only the issue of Moncrief’s suspension and not the issue of his discharge. The Union asserted that because both the suspension and the discharge arose from the same event, both issues were properly before the arbitrator. The arbitrator agreed with the Union, ruling that although “this action, when grieved, was categorized as a suspension pending investigation, the action was, to use the Company’s terminology, ‘converted’ to discharge. It follows that the grievance was automatically converted as well.” The arbitrator therefore determined the issue to be whether the suspension and discharge of Moncrief were for just cause. It determined that the Company’s action was without just cause and awarded Moncrief reinstatement and back pay.
The Company then sued in the Northern District of Alabama for a declaratory judgment and to set aside the arbitral award to the extent that it determined matters involving Moncrief’s discharge. The Union moved for summary judgment based on the collective bargaining agreement and the ar-bitral award. The trial court denied the motion, ruling that the arbitrator lacked jurisdiction because the Union did not present the discharge grievance in accordance with contract procedures. The case proceeded to trial confined to the issue whether the Company had waived those procedures. After trial, the court found neither waiver nor estoppel and declared the arbitrator’s award void as having been made without jurisdiction. The Union appeals. We reverse.
*962It is well-settled that the federal labor laws embody a policy favoring arbitration as a substitute for industrial strife. See United Steelworkers v. American Manufacturing Co., 363 U.S. 564, 80 S.Ct. 1343, 4 L.Ed.2d 1403 (1960); United Steelworkers v. Warrior & Gulf Navigation Co., 363 U.S. 574, 80 S.Ct. 1347, 4 L.Ed.2d 1409 (1960); United Steelworkers v. Enterprise Wheel & Car Corp., 363 U.S. 593, 80 S.Ct. 1358, 4 L.Ed.2d 1424 (1960). The Steelworkers Trilogy limits the role of the courts in those disputes subject to arbitration under a collective bargaining agreement. Generally speaking, the court merely ascertains “whether the party seeking arbitration is making a claim which on its face is governed by the contract,” American Manufacturing Co., 363 U.S. at 568, 80 S.Ct. at 1346, without regard to the merits of the claim; courts must give the arbitration clause a broad reading, with all doubts resolved in favor of the arbitration clause’s coverage of the dispute. Warrior & Gulf Navigation Co., 363 U.S. at 582-83, 80 S.Ct. at 1352-53. Moreover, because the parties have bargained for the arbitrator’s construction of the agreement, courts cannot overrule his decision merely because their interpretation of the contract is different from his; the arbitrator’s words must “manifest an infidelity” to the collective bargaining agreement. Enterprise Wheel & Car Corp., 363 U.S. at 597-99, 80 S.Ct. at 1361-62.
The Supreme Court has applied these principles to questions of so-called “procedural arbitrability” as well, that is, to questions whether the parties have met the procedural prerequisites that condition the duty to arbitrate under the collective bargaining agreement. In John Wiley & Sons v. Livingston, 376 U.S. 543, 557, 84 S.Ct. 909, 918, 11 L.Ed.2d 898 (1964), the Court reasoned as follows:
Doubt whether grievance procedures or some part of them apply to a particular dispute, whether such procedures have been followed or excused, or whether the unexcused failure to follow them avoids the duty to arbitrate cannot ordinarily be answered without consideration of the merits of the dispute which is presented for arbitration. ... It would be a curious rule which required that inter-'' twined issues of “substance” and “procedure” growing out of a single dispute and raising the same questions on the same facts had to be carved up between two different forums, one deciding after the other. Neither logic nor considerations of policy compel such a result.
Therefore, the court held, once the court has determined that the subject matter of the dispute is subject to arbitration, it is for the arbitrator, not the court, to decide whether the procedural prerequisites (i. e., the grievance procedure) have been fulfilled.
The district court, in denying the Union’s motion for summary judgment, ruled that “it appears that the arbitrator lacked jurisdiction under the collective bargaining agreement to properly hear the discharge grievance because it was not presented in accordance with the contract procedures.” The court neglected to consider, however, that the arbitrator had already determined the issue of “procedural arbitrability” in favor of the Union. In so doing, the district court considered the merits of the dispute. At least implicitly, it rejected the arbitrator’s conclusion that the discharge was “a conversion of the suspension and essentially the same.” Whether the discharge was merely a continuation of the original disciplinary measure, however, depends on Moncrief’s activities, the Company’s responses, and the significance of each under the contract. Consideration of these matters is to be left to the arbitrator.
The Company attempts to distinguish John Wiley & Sons on the basis that the Company did not agree to arbitrate any issue related to the discharge. It argues that John Wiley & Sons and the other cases cited by the Union all involved “cases where grievances had been filed involving the matter subject to arbitration. Here, there was no grievance filed and the Company did not agree to submit the issue of discharge to arbitration!” This argument misunderstands the lessons of John Wiley & *963Sons and the Steelworkers Trilogy. If the subject matter of the dispute is arguably arbitrable (resolving all doubts in favor of coverage), then it is for the arbitrator to decide whether or not the dispute may be arbitrated. The Company should have addressed its arguments that the proper procedures were not followed to the arbitrator, not to the courts. See Palestine Telephone Co. v. Local 1506, IBEW, 379 F.2d 234, 240 (5th Cir. 1967).
The Company’s argument could be construed as asserting that even if the arbitrator was the appropriate forum to determine procedural arbitrability, the court should set aside the award because the arbitrator was wrong. That argument must fail. We cannot say that the arbitrator’s words manifest an infidelity to the collective bargaining agreement. Cf. General Warehousemen’s Local 767 v. Standard Brands, Inc., 579 F.2d. 1282, 1292-93 (5th Cir. 1978) (en banc). As the Court stated in Enterprise Wheel & Car Corp., 363 U.S. at 599, 80 S.Ct. at 1362:
It is the arbitrator’s construction which was bargained for; and so far as the arbitrator’s decision concerns construction of the contract, the courts have no business overruling him because their interpretation of the contract is different from his.
The district court was therefore wrong to substitute its judgment for that of the arbitrator on the question whether the grievance about Moncrief’s discharge had been properly submitted to arbitration.
REVERSED.