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Theorem raleqi 2630
 Description: Equality inference for restricted universal qualifier. (Contributed by Paul Chapman, 22-Jun-2011.)
Hypothesis
Ref Expression
raleq1i.1
Assertion
Ref Expression
raleqi
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem raleqi
StepHypRef Expression
1 raleq1i.1 . 2
2 raleq 2626 . 2
31, 2ax-mp 5 1
 Colors of variables: wff set class Syntax hints:   wb 104   wceq 1331  wral 2416 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421 This theorem is referenced by:  ralrab2  2849  ralprg  3574  raltpg  3576  omsinds  4535  ralxp  4682  ralrnmpo  5885  fzprval  9869  fztpval  9870  seq3f1olemp  10282  zsumdc  11160  infssuzex  11649  2prm  11815  nninfsellemdc  13236  nninfsellemsuc  13238
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