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Theorem ralimiaa 2688
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 423 . 2 (x A → (φψ))
32ralimia 2687 1 (x A φx A ψ)
Colors of variables: wff setvar class
Syntax hints:  wi 4   wa 358   wcel 1710  wral 2614
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-ral 2619
This theorem is referenced by: (None)
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