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Theorem isfin4 8182
 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 3437 . . . . 5
2 breq2 4219 . . . . 5
31, 2anbi12d 693 . . . 4
43exbidv 1637 . . 3
54notbid 287 . 2
6 df-fin4 8172 . 2 FinIV
75, 6elab2g 3086 1 FinIV
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 178   wa 360  wex 1551   wceq 1653   wcel 1726   wpss 3323   class class class wbr 4215   cen 7109  FinIVcfin4 8165 This theorem is referenced by:  fin4i  8183  fin4en1  8194  ssfin4  8195  infpssALT  8198  isfin4-2  8199 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-pss 3338  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-br 4216  df-fin4 8172
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