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Theorem isfin4 8680
 Description: Definition of a IV-finite set. (Contributed by Stefan O'Rear, 16-May-2015.)
Assertion
Ref Expression
isfin4 FinIV
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem isfin4
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 psseq2 3577 . . . . 5
2 breq2 4441 . . . . 5
31, 2anbi12d 710 . . . 4
43exbidv 1701 . . 3
54notbid 294 . 2
6 df-fin4 8670 . 2 FinIV
75, 6elab2g 3234 1 FinIV
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 184   wa 369   wceq 1383  wex 1599   wcel 1804   wpss 3462   class class class wbr 4437   cen 7515  FinIVcfin4 8663 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-10 1823  ax-11 1828  ax-12 1840  ax-13 1985  ax-ext 2421 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 976  df-tru 1386  df-ex 1600  df-nf 1604  df-sb 1727  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2593  df-ne 2640  df-rab 2802  df-v 3097  df-dif 3464  df-un 3466  df-in 3468  df-ss 3475  df-pss 3477  df-nul 3771  df-if 3927  df-sn 4015  df-pr 4017  df-op 4021  df-br 4438  df-fin4 8670 This theorem is referenced by:  fin4i  8681  fin4en1  8692  ssfin4  8693  infpssALT  8696  isfin4-2  8697
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