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Theorem riotaeqbidv 5627
 Description: Equality deduction for restricted universal quantifier. (Contributed by NM, 15-Sep-2011.)
Hypotheses
Ref Expression
riotaeqbidv.1
riotaeqbidv.2
Assertion
Ref Expression
riotaeqbidv
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()   ()

Proof of Theorem riotaeqbidv
StepHypRef Expression
1 riotaeqbidv.2 . . 3
21riotabidv 5626 . 2
3 riotaeqbidv.1 . . 3
43riotaeqdv 5625 . 2
52, 4eqtrd 2121 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104   wceq 1290  crio 5623 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071 This theorem depends on definitions:  df-bi 116  df-tru 1293  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-rex 2366  df-uni 3662  df-iota 4995  df-riota 5624 This theorem is referenced by:  acexmidlemab  5662
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