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Theorem elunif 29583
 Description: A version of eluni 4082 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 4082 . 2
2 elunif.1 . . . . 5
3 nfcv 2569 . . . . 5
42, 3nfel 2577 . . . 4
5 elunif.2 . . . . 5
63, 5nfel 2577 . . . 4
74, 6nfan 1859 . . 3
8 nfv 1672 . . 3
9 eleq2 2494 . . . 4
10 eleq1 2493 . . . 4
119, 10anbi12d 703 . . 3
127, 8, 11cbvex 1969 . 2
131, 12bitri 249 1
 Colors of variables: wff setvar class Syntax hints:   wb 184   wa 369  wex 1589   wcel 1755  wnfc 2556  cuni 4079 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1594  ax-4 1605  ax-5 1669  ax-6 1707  ax-7 1727  ax-10 1774  ax-11 1779  ax-12 1791  ax-13 1942  ax-ext 2414 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1365  df-ex 1590  df-nf 1593  df-sb 1700  df-clab 2420  df-cleq 2426  df-clel 2429  df-nfc 2558  df-v 2964  df-uni 4080 This theorem is referenced by:  stoweidlem46  29687  stoweidlem57  29698
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