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Theorem raleqbii 2353
 Description: Equality deduction for restricted universal quantifier, changing both formula and quantifier domain. Inference form. (Contributed by David Moews, 1-May-2017.)
Hypotheses
Ref Expression
raleqbii.1
raleqbii.2
Assertion
Ref Expression
raleqbii

Proof of Theorem raleqbii
StepHypRef Expression
1 raleqbii.1 . . . 4
21eleq2i 2120 . . 3
3 raleqbii.2 . . 3
42, 3imbi12i 232 . 2
54ralbii2 2351 1
 Colors of variables: wff set class Syntax hints:   wb 102   wceq 1259   wcel 1409  wral 2323 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-4 1416  ax-17 1435  ax-ial 1443  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-cleq 2049  df-clel 2052  df-ral 2328 This theorem is referenced by: (None)
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