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Theorem dfepfr 4568
 Description: An alternate way of saying that the epsilon relation is well-founded. (Contributed by NM, 17-Feb-2004.) (Revised by Mario Carneiro, 23-Jun-2015.)
Assertion
Ref Expression
dfepfr
Distinct variable group:   ,,

Proof of Theorem dfepfr
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dffr2 4548 . 2
2 epel 4498 . . . . . . . . 9
32a1i 11 . . . . . . . 8
43rabbiia 2947 . . . . . . 7
5 dfin5 3329 . . . . . . 7
64, 5eqtr4i 2460 . . . . . 6
76eqeq1i 2444 . . . . 5
87rexbii 2731 . . . 4
98imbi2i 305 . . 3
109albii 1576 . 2
111, 10bitri 242 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360  wal 1550   wceq 1653   wne 2600  wrex 2707  crab 2710   cin 3320   wss 3321  c0 3629   class class class wbr 4213   cep 4493   wfr 4539 This theorem is referenced by:  onfr  4621  zfregfr  7571  onfrALTlem3  28631  onfrALT  28636  onfrALTlem3VD  29000  onfrALTVD  29004 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418  ax-sep 4331  ax-nul 4339  ax-pr 4404 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2286  df-mo 2287  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-ne 2602  df-ral 2711  df-rex 2712  df-rab 2715  df-v 2959  df-dif 3324  df-un 3326  df-in 3328  df-ss 3335  df-nul 3630  df-if 3741  df-sn 3821  df-pr 3822  df-op 3824  df-br 4214  df-opab 4268  df-eprel 4495  df-fr 4542
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