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Theorem isfin7 8573
 Description: Definition of a VII-finite set. (Contributed by Stefan O'Rear, 16-May-2015.)
Assertion
Ref Expression
isfin7 FinVII
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem isfin7
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 breq1 4395 . . . 4
21rexbidv 2848 . . 3
32notbid 294 . 2
4 df-fin7 8563 . 2 FinVII
53, 4elab2g 3207 1 FinVII
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 184   wceq 1370   wcel 1758  wrex 2796   cdif 3425   class class class wbr 4392  con0 4819  com 6578   cen 7409  FinVIIcfin7 8556 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1952  ax-ext 2430 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2601  df-ral 2800  df-rex 2801  df-rab 2804  df-v 3072  df-dif 3431  df-un 3433  df-in 3435  df-ss 3442  df-nul 3738  df-if 3892  df-sn 3978  df-pr 3980  df-op 3984  df-br 4393  df-fin7 8563 This theorem is referenced by:  fin17  8666  fin67  8667  isfin7-2  8668
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