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Theorem rexbiia 2333
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 427 . 2 ((x A φ) ↔ (x A ψ))
32rexbii2 2329 1 (x A φx A ψ)
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98   wcel 1390  wrex 2301
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-ial 1424
This theorem depends on definitions:  df-bi 110  df-rex 2306
This theorem is referenced by:  2rexbiia  2334  ceqsrexbv  2669  reu8  2731  reldm  5754  prarloclem3  6480  recexgt0  7364
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