Theorem bj-sylgt2 36619

Description: Uncurried (imported) form of sylgt 1822. (Contributed by BJ, 2-May-2019.)

Assertion

Ref	Expression
bj-sylgt2	⊢ ((∀𝑥(𝜓 → 𝜒) ∧ (𝜑 → ∀𝑥𝜓)) → (𝜑 → ∀𝑥𝜒))

Proof of Theorem bj-sylgt2

Step	Hyp	Ref	Expression
1		sylgt 1822	. 2 ⊢ (∀𝑥(𝜓 → 𝜒) → ((𝜑 → ∀𝑥𝜓) → (𝜑 → ∀𝑥𝜒)))
2	1	imp 406	1 ⊢ ((∀𝑥(𝜓 → 𝜒) ∧ (𝜑 → ∀𝑥𝜓)) → (𝜑 → ∀𝑥𝜒))

Syntax hints:   → wi 4   ∧ wa 395  ∀wal 1538

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-4 1809

This theorem depends on definitions:  df-bi 207  df-an 396

This theorem is referenced by: (None)