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Theorem frc 4540
 Description: Property of well-founded relation (one direction of definition using class variables). (Contributed by NM, 17-Feb-2004.) (Revised by Mario Carneiro, 19-Nov-2014.)
Hypothesis
Ref Expression
frc.1
Assertion
Ref Expression
frc
Distinct variable groups:   ,,   ,,   ,,

Proof of Theorem frc
StepHypRef Expression
1 frc.1 . . . 4
2 fri 4536 . . . 4
31, 2mpanl1 662 . . 3
433impb 1149 . 2
5 rabeq0 3641 . . 3
65rexbii 2722 . 2
74, 6sylibr 204 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 359   w3a 936   wceq 1652   wcel 1725   wne 2598  wral 2697  wrex 2698  crab 2701  cvv 2948   wss 3312  c0 3620   class class class wbr 4204   wfr 4530 This theorem is referenced by:  frirr  4551  epfrc  4560 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-in 3319  df-ss 3326  df-nul 3621  df-fr 4533
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