Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  rexeqbidva Unicode version

Theorem rexeqbidva 3071
 Description: Equality deduction for restricted universal quantifier. (Contributed by Mario Carneiro, 5-Jan-2017.)
Hypotheses
Ref Expression
raleqbidva.1
raleqbidva.2
Assertion
Ref Expression
rexeqbidva
Distinct variable groups:   ,   ,   ,

Proof of Theorem rexeqbidva
StepHypRef Expression
1 raleqbidva.2 . . 3
21rexbidva 2965 . 2
3 raleqbidva.1 . . 3
43rexeqdv 3061 . 2
52, 4bitrd 253 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  e.wcel 1818  E.wrex 2808 This theorem is referenced by:  catpropd  15104  istrkgb  23852  istrkgcb  23853  istrkge  23854  isperp  24089  perpcom  24090  eengtrkg  24288  eengtrkge  24289  afsval  28551 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rex 2813
 Copyright terms: Public domain W3C validator