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Theorem elunif 27664
 Description: A version of eluni 4019 using bound-variable hypotheses instead of distinct variable conditions. (Contributed by Glauco Siliprandi, 20-Apr-2017.)
Hypotheses
Ref Expression
elunif.1
elunif.2
Assertion
Ref Expression
elunif
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem elunif
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eluni 4019 . 2
2 elunif.1 . . . . 5
3 nfcv 2573 . . . . 5
42, 3nfel 2581 . . . 4
5 elunif.2 . . . . 5
63, 5nfel 2581 . . . 4
74, 6nfan 1847 . . 3
8 nfv 1630 . . 3
9 eleq2 2498 . . . 4
10 eleq1 2497 . . . 4
119, 10anbi12d 693 . . 3
127, 8, 11cbvex 1984 . 2
131, 12bitri 242 1
 Colors of variables: wff set class Syntax hints:   wb 178   wa 360  wex 1551   wcel 1726  wnfc 2560  cuni 4016 This theorem is referenced by:  stoweidlem46  27772  stoweidlem57  27783 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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 2418 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 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-v 2959  df-uni 4017
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