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Theorem isfin1a 8693
 Description: Definition of a Ia-finite set. (Contributed by Stefan O'Rear, 16-May-2015.)
Assertion
Ref Expression
isfin1a
Distinct variable group:   ,

Proof of Theorem isfin1a
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 pweq 4015 . . 3
2 difeq1 3614 . . . . 5
32eleq1d 2526 . . . 4
43orbi2d 701 . . 3
51, 4raleqbidv 3068 . 2
6 df-fin1a 8686 . 2
75, 6elab2g 3248 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  \/wo 368  =wceq 1395  e.wcel 1818  A.wral 2807  \cdif 3472  ~Pcpw 4012   cfn 7536   cfin1a 8679 This theorem is referenced by:  fin1ai  8694  fin11a  8784  enfin1ai  8785 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-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rab 2816  df-v 3111  df-dif 3478  df-in 3482  df-ss 3489  df-pw 4014  df-fin1a 8686
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