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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.
StepHypRef Expression
1 breq1 4455 . . . 4
21rexbidv 2968 . . 3
32notbid 294 . 2
4 df-fin7 8692 . 2
53, 4elab2g 3248 1
 Colors of variables: wff setvar class 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
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