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Theorem raleqi 2558
 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 2554 . 2
31, 2ax-mp 7 1
 Colors of variables: wff set class Syntax hints:   wb 103   wceq 1285  wral 2353 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-cleq 2076  df-clel 2079  df-nfc 2212  df-ral 2358 This theorem is referenced by:  ralrab2  2767  ralprg  3462  raltpg  3464  ralxp  4528  ralrnmpt2  5667  fzprval  9211  fztpval  9212  infssuzex  10536  2prm  10700
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