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Theorem raleqbidva 3033
 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 2841 . 2
3 raleqbidva.1 . . 3
43raleqdv 3023 . 2
52, 4bitrd 253 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369   wceq 1370   wcel 1758  wral 2796 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-ext 2431 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-cleq 2444  df-clel 2447  df-nfc 2602  df-ral 2801 This theorem is referenced by:  swrdspsleq  12455  catpropd  14762  cidpropd  14763  funcpropd  14924  fullpropd  14944  natpropd  15000  gsumpropd2lem  15619  istrkgc  23043  istrkgb  23044  istrkgcb  23045  istrkge  23046  iscgrg  23096  isperp  23243  rngurd  26396  clwlkisclwwlk  30594
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