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Theorem elunif 27790
 Description: A version of eluni 3846 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 3846 . 2
2 elunif.1 . . . . 5
3 nfcv 2432 . . . . 5
42, 3nfel 2440 . . . 4
5 elunif.2 . . . . 5
63, 5nfel 2440 . . . 4
74, 6nfan 1783 . . 3
8 nfv 1609 . . 3
9 eleq2 2357 . . . 4
10 eleq1 2356 . . . 4
119, 10anbi12d 691 . . 3
127, 8, 11cbvex 1938 . 2
131, 12bitri 240 1
 Colors of variables: wff set class Syntax hints:   wb 176   wa 358  wex 1531   wceq 1632   wcel 1696  wnfc 2419  cuni 3843 This theorem is referenced by:  stoweidlem46  27898  stoweidlem57  27909 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-uni 3844
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