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Theorem sylgt 1898
Description: Closed form of sylg 1899. (Contributed by BJ, 2-May-2019.)
Assertion
Ref Expression
sylgt (∀𝑥(𝜓𝜒) → ((𝜑 → ∀𝑥𝜓) → (𝜑 → ∀𝑥𝜒)))

Proof of Theorem sylgt
StepHypRef Expression
1 alim 1887 . 2 (∀𝑥(𝜓𝜒) → (∀𝑥𝜓 → ∀𝑥𝜒))
21imim2d 57 1 (∀𝑥(𝜓𝜒) → ((𝜑 → ∀𝑥𝜓) → (𝜑 → ∀𝑥𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1630
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-4 1886
This theorem is referenced by:  bj-sylgt2  32930  bj-nexdh  32935  bj-alrim  33012  bj-cbv3ta  33039
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