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Theorem rexeqbii 2736
Description: Equality deduction for restricted existential quantifier, changing both formula and quantifier domain. Inference form. (Contributed by David Moews, 1-May-2017.)
Hypotheses
Ref Expression
raleqbii.1  |-  A  =  B
raleqbii.2  |-  ( ps  <->  ch )
Assertion
Ref Expression
rexeqbii  |-  ( E. x  e.  A  ps  <->  E. x  e.  B  ch )

Proof of Theorem rexeqbii
StepHypRef Expression
1 raleqbii.1 . . . 4  |-  A  =  B
21eleq2i 2500 . . 3  |-  ( x  e.  A  <->  x  e.  B )
3 raleqbii.2 . . 3  |-  ( ps  <->  ch )
42, 3anbi12i 679 . 2  |-  ( ( x  e.  A  /\  ps )  <->  ( x  e.  B  /\  ch )
)
54rexbii2 2734 1  |-  ( E. x  e.  A  ps  <->  E. x  e.  B  ch )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    = wceq 1652    e. wcel 1725   E.wrex 2706
This theorem is referenced by:  bnj882  29297
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-11 1761  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-cleq 2429  df-clel 2432  df-rex 2711
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