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Theorem raleqbii 2902
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 2535 . . 3
3 raleqbii.2 . . 3
42, 3imbi12i 326 . 2
54ralbii2 2886 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  =wceq 1395  e.wcel 1818  A.wral 2807
This theorem is referenced by:  ply1coe  18337  ordtbaslem  19689  iscusp2  20805  elghomOLD  25365  wfrlem5  29347  frrlem5  29391  iscrngo2  30395  tendoset  36485
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-cleq 2449  df-clel 2452  df-ral 2812
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