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Theorem isfin1a 8177
 Description: Definition of a Ia-finite set. (Contributed by Stefan O'Rear, 16-May-2015.)
Assertion
Ref Expression
isfin1a FinIa
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem isfin1a
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 pweq 3804 . . 3
2 difeq1 3460 . . . . 5
32eleq1d 2504 . . . 4
43orbi2d 684 . . 3
51, 4raleqbidv 2918 . 2
6 df-fin1a 8170 . 2 FinIa
75, 6elab2g 3086 1 FinIa
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wo 359   wceq 1653   wcel 1726  wral 2707   cdif 3319  cpw 3801  cfn 7112  FinIacfin1a 8163 This theorem is referenced by:  fin1ai  8178  fin11a  8268  enfin1ai  8269 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-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rab 2716  df-v 2960  df-dif 3325  df-in 3329  df-ss 3336  df-pw 3803  df-fin1a 8170
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