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Theorem sylgt 1739
Description: Closed form of sylg 1740. (Contributed by BJ, 2-May-2019.)
Assertion
Ref Expression
sylgt (∀𝑥(𝜓𝜒) → ((𝜑 → ∀𝑥𝜓) → (𝜑 → ∀𝑥𝜒)))

Proof of Theorem sylgt
StepHypRef Expression
1 alim 1729 . 2 (∀𝑥(𝜓𝜒) → (∀𝑥𝜓 → ∀𝑥𝜒))
21imim2d 55 1 (∀𝑥(𝜓𝜒) → ((𝜑 → ∀𝑥𝜓) → (𝜑 → ∀𝑥𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1473
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-4 1728
This theorem is referenced by:  bj-sylgt2  31786  bj-nexdh  31790  bj-alrim  31870  bj-cbv3ta  31897
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