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Theorem ralimiaa 2377
Description: Inference quantifying both antecedent and consequent. (Contributed by NM, 4-Aug-2007.)
Hypothesis
Ref Expression
ralimiaa.1 ((x A φ) → ψ)
Assertion
Ref Expression
ralimiaa (x A φx A ψ)

Proof of Theorem ralimiaa
StepHypRef Expression
1 ralimiaa.1 . . 3 ((x A φ) → ψ)
21ex 108 . 2 (x A → (φψ))
32ralimia 2376 1 (x A φx A ψ)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97   wcel 1390  wral 2300
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
This theorem depends on definitions:  df-bi 110  df-ral 2305
This theorem is referenced by:  ralrnmpt  5252  rexrnmpt  5253  acexmidlem2  5452
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