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Theorem ralimiaa 2400
Description: Inference quantifying both antecedent and consequent. (Contributed by NM, 4-Aug-2007.)
Hypothesis
Ref Expression
ralimiaa.1 ((𝑥𝐴𝜑) → 𝜓)
Assertion
Ref Expression
ralimiaa (∀𝑥𝐴 𝜑 → ∀𝑥𝐴 𝜓)

Proof of Theorem ralimiaa
StepHypRef Expression
1 ralimiaa.1 . . 3 ((𝑥𝐴𝜑) → 𝜓)
21ex 112 . 2 (𝑥𝐴 → (𝜑𝜓))
32ralimia 2399 1 (∀𝑥𝐴 𝜑 → ∀𝑥𝐴 𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101  wcel 1409  wral 2323
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354
This theorem depends on definitions:  df-bi 114  df-ral 2328
This theorem is referenced by:  ralrnmpt  5337  rexrnmpt  5338  acexmidlem2  5537
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