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Theorem isfin4 8698
Description: Definition of a IV-finite set. (Contributed by Stefan O'Rear, 16-May-2015.)
Assertion
Ref Expression
isfin4
Distinct variable group:   ,

Proof of Theorem isfin4
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 psseq2 3591 . . . . 5
2 breq2 4456 . . . . 5
31, 2anbi12d 710 . . . 4
43exbidv 1714 . . 3
54notbid 294 . 2
6 df-fin4 8688 . 2
75, 6elab2g 3248 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  E.wex 1612  e.wcel 1818  C.wpss 3476   class class class wbr 4452   cen 7533   cfin4 8681
This theorem is referenced by:  fin4i  8699  fin4en1  8710  ssfin4  8711  infpssALT  8714  isfin4-2  8715
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-ne 2654  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-pss 3491  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-fin4 8688
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