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Theorem isacn 7930
 Description: The property of being a choice set of length . (Contributed by Mario Carneiro, 31-Aug-2015.)
Assertion
Ref Expression
isacn AC
Distinct variable groups:   ,,,   ,,,
Allowed substitution hints:   (,,)   (,,)

Proof of Theorem isacn
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 pweq 3804 . . . . . . 7
21difeq1d 3466 . . . . . 6
32oveq1d 6099 . . . . 5
43raleqdv 2912 . . . 4
54anbi2d 686 . . 3
6 df-acn 7834 . . 3 AC
75, 6elab2g 3086 . 2 AC
8 elex 2966 . . 3
9 biid 229 . . . 4
109baib 873 . . 3
118, 10syl 16 . 2
127, 11sylan9bb 682 1 AC
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360  wex 1551   wceq 1653   wcel 1726  wral 2707  cvv 2958   cdif 3319  c0 3630  cpw 3801  csn 3816  cfv 5457  (class class class)co 6084   cmap 7021  AC wacn 7830 This theorem is referenced by:  acni  7931  numacn  7935  finacn  7936  acndom  7937  acndom2  7940  acncc  8325 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-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-pw 3803  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4216  df-iota 5421  df-fv 5465  df-ov 6087  df-acn 7834
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