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Theorem raleqbidva 2910
 Description: Equality deduction for restricted universal quantifier. (Contributed by Mario Carneiro, 5-Jan-2017.)
Hypotheses
Ref Expression
raleqbidva.1
raleqbidva.2
Assertion
Ref Expression
raleqbidva
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem raleqbidva
StepHypRef Expression
1 raleqbidva.2 . . 3
21ralbidva 2713 . 2
3 raleqbidva.1 . . 3
43raleqdv 2902 . 2
52, 4bitrd 245 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   wceq 1652   wcel 1725  wral 2697 This theorem is referenced by:  catpropd  13927  cidpropd  13928  funcpropd  14089  fullpropd  14109  natpropd  14165  gsumpropd2lem  24212 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702
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