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Theorem epfrc 4870
 Description: A subset of an epsilon-founded class has a minimal element. (Contributed by NM, 17-Feb-2004.) (Revised by David Abernethy, 22-Feb-2011.)
Hypothesis
Ref Expression
epfrc.1
Assertion
Ref Expression
epfrc
Distinct variable groups:   ,   ,

Proof of Theorem epfrc
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 epfrc.1 . . 3
21frc 4850 . 2
3 dfin5 3483 . . . . 5
4 epel 4799 . . . . . . 7
54a1i 11 . . . . . 6
65rabbiia 3098 . . . . 5
73, 6eqtr4i 2489 . . . 4
87eqeq1i 2464 . . 3
98rexbii 2959 . 2
102, 9sylibr 212 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\w3a 973  =wceq 1395  e.wcel 1818  =/=wne 2652  E.wrex 2808  {crab 2811   cvv 3109  i^icin 3474  C_wss 3475   c0 3784   class class class wbr 4452   cep 4794  Frwfr 4840 This theorem is referenced by:  wefrc  4878  onfr  4922  epfrs  8183 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-opab 4511  df-eprel 4796  df-fr 4843
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