Theorem zfregfr 8050

Description: The epsilon relation is well-founded on any class. (Contributed by NM, 26-Nov-1995.)

Assertion

Ref	Expression
zfregfr

Proof of Theorem zfregfr

Dummy variables are mutually distinct and distinct from all other variables.

Step	Hyp	Ref	Expression
1		dfepfr 4869	. 2
2		vex 3112	. . . 4
3	2	zfreg2 8043	. . 3
4	3	adantl 466	. 2
5	1, 4	mpgbir 1622	1

Syntax hints:  ->wi 4  /\wa 369  =wceq 1395  =/=wne 2652  E.wrex 2808  i^icin 3474  C_wss 3475  c0 3784  cep 4794  Frwfr 4840

This theorem is referenced by:  en2lp  8051  dford2  8058  noinfep  8097  noinfepOLD  8098  zfregs  8184  dford5reg  29214  trelpss  31364  bnj852  33979

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  ax-reg 8039

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