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Theorem rexbiia 2308
 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 2304 1 (x A φx A ψ)
 Colors of variables: wff set class Syntax hints:   → wi 4   ↔ wb 98   ∈ wcel 1366  ∃wrex 2276 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 1309  ax-gen 1311  ax-ie1 1355  ax-ie2 1356  ax-4 1373  ax-ial 1400 This theorem depends on definitions:  df-bi 110  df-rex 2281 This theorem is referenced by:  2rexbiia  2309  ceqsrexbv  2643  reu8  2705  reldm  5723  prarloclem3  6337  recexgt0  7167
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