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Theorem elunif 36771
 Description: A version of eluni 4194 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 4194 . 2
2 elunif.1 . . . . 5
3 nfcv 2564 . . . . 5
42, 3nfel 2577 . . . 4
5 elunif.2 . . . . 5
63, 5nfel 2577 . . . 4
74, 6nfan 1956 . . 3
8 nfv 1728 . . 3
9 eleq2 2475 . . . 4
10 eleq1 2474 . . . 4
119, 10anbi12d 709 . . 3
127, 8, 11cbvex 2049 . 2
131, 12bitri 249 1
 Colors of variables: wff setvar class Syntax hints:   wb 184   wa 367  wex 1633   wcel 1842  wnfc 2550  cuni 4191 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-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-v 3061  df-uni 4192 This theorem is referenced by:  stoweidlem46  37196  stoweidlem57  37207
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