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Theorem isfin1a 8624
 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 3957 . . 3
2 difeq1 3553 . . . . 5
32eleq1d 2471 . . . 4
43orbi2d 700 . . 3
51, 4raleqbidv 3017 . 2
6 df-fin1a 8617 . 2 FinIa
75, 6elab2g 3197 1 FinIa
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wo 366   wceq 1405   wcel 1842  wral 2753   cdif 3410  cpw 3954  cfn 7474  FinIacfin1a 8610 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380 This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-ral 2758  df-rab 2762  df-v 3060  df-dif 3416  df-in 3420  df-ss 3427  df-pw 3956  df-fin1a 8617 This theorem is referenced by:  fin1ai  8625  fin11a  8715  enfin1ai  8716
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