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Theorem rexbiia 2647
Description: Inference adding restricted existential quantifier to both sides of an equivalence. (Contributed by NM, 26-Oct-1999.)
Hypothesis
Ref Expression
ralbiia.1 (x A → (φψ))
Assertion
Ref Expression
rexbiia (x A φx A ψ)

Proof of Theorem rexbiia
StepHypRef Expression
1 ralbiia.1 . . 3 (x A → (φψ))
21pm5.32i 618 . 2 ((x A φ) ↔ (x A ψ))
32rexbii2 2643 1 (x A φx A ψ)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176   wcel 1710  wrex 2615
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-rex 2620
This theorem is referenced by:  2rexbiia  2648  ceqsrexbv  2973  reu8  3032  phialllem1  4616  finnc  6243  nchoicelem11  6299  nchoicelem16  6304
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