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Theorem raleqbidv 2562
 Description: Equality deduction for restricted universal quantifier. (Contributed by NM, 6-Nov-2007.)
Hypotheses
Ref Expression
raleqbidv.1
raleqbidv.2
Assertion
Ref Expression
raleqbidv
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem raleqbidv
StepHypRef Expression
1 raleqbidv.1 . . 3
21raleqdv 2556 . 2
3 raleqbidv.2 . . 3
43ralbidv 2369 . 2
52, 4bitrd 186 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 103   wceq 1285  wral 2349 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 2064 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-cleq 2075  df-clel 2078  df-nfc 2209  df-ral 2354 This theorem is referenced by:  ofrfval  5745  fmpt2x  5851  tfrlemi1  5975  supeq123d  6453  cvg1nlemcau  9997  cvg1nlemres  9998  cau3lem  10127  sscoll2  10926
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