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Theorem ra4v 3871
Description: Version of ra4 3872 with a disjoint variable condition, requiring fewer axioms. This is stdpc5v 1932 for a restricted domain. (Contributed by BJ, 27-Mar-2020.)
Assertion
Ref Expression
ra4v (∀𝑥𝐴 (𝜑𝜓) → (𝜑 → ∀𝑥𝐴 𝜓))
Distinct variable group:   𝜑,𝑥
Allowed substitution hints:   𝜓(𝑥)   𝐴(𝑥)

Proof of Theorem ra4v
StepHypRef Expression
1 r19.21v 3179 . 2 (∀𝑥𝐴 (𝜑𝜓) ↔ (𝜑 → ∀𝑥𝐴 𝜓))
21biimpi 217 1 (∀𝑥𝐴 (𝜑𝜓) → (𝜑 → ∀𝑥𝐴 𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wral 3142
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1904
This theorem depends on definitions:  df-bi 208  df-ex 1774  df-ral 3147
This theorem is referenced by:  wfr3g  7947  frr3g  33005
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