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Theorem bj-sylgt2 32726
Description: Uncurried (imported) form of sylgt 1789. (Contributed by BJ, 2-May-2019.)
Assertion
Ref Expression
bj-sylgt2 ((∀𝑥(𝜓𝜒) ∧ (𝜑 → ∀𝑥𝜓)) → (𝜑 → ∀𝑥𝜒))

Proof of Theorem bj-sylgt2
StepHypRef Expression
1 sylgt 1789 . 2 (∀𝑥(𝜓𝜒) → ((𝜑 → ∀𝑥𝜓) → (𝜑 → ∀𝑥𝜒)))
21imp 444 1 ((∀𝑥(𝜓𝜒) ∧ (𝜑 → ∀𝑥𝜓)) → (𝜑 → ∀𝑥𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383  wal 1521
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-4 1777
This theorem depends on definitions:  df-bi 197  df-an 385
This theorem is referenced by: (None)
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