Theorem isfin7 8702

Description: Definition of a VII-finite set. (Contributed by Stefan O'Rear, 16-May-2015.)

Assertion

Ref	Expression
isfin7

Distinct variable group:   ,

Proof of Theorem isfin7

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		breq1 4455	. . . 4
2	1	rexbidv 2968	. . 3
3	2	notbid 294	. 2
4		df-fin7 8692	. 2
5	3, 4	elab2g 3248	1

Syntax hints:  -.wn 3  ->wi 4  <->wb 184  =wceq 1395  e.wcel 1818  E.wrex 2808  \cdif 3472   class class class wbr 4452  con0 4883  com 6700  cen 7533  cfin7 8685

This theorem is referenced by:  fin17  8795  fin67  8796  isfin7-2  8797

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-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

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-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  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-fin7 8692