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Theorem frc 4805
 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 4801 . . . 4
31, 2mpanl1 694 . . 3
433impb 1227 . 2
5 rabeq0 3757 . . 3
65rexbii 2881 . 2
74, 6sylibr 217 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 376   w3a 1007   wceq 1452   wcel 1904   wne 2641  wral 2756  wrex 2757  crab 2760  cvv 3031   wss 3390  c0 3722   class class class wbr 4395   wfr 4795 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ne 2643  df-ral 2761  df-rex 2762  df-rab 2765  df-v 3033  df-dif 3393  df-in 3397  df-ss 3404  df-nul 3723  df-fr 4798 This theorem is referenced by:  frirr  4816  epfrc  4825
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