Theorem bj-sylgt2

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

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

Proof

Step	Hyp	Ref	Expression
1		sylgt	⊢ ( ∀ 𝑥 ( 𝜓 → 𝜒 ) → ( ( 𝜑 → ∀ 𝑥 𝜓 ) → ( 𝜑 → ∀ 𝑥 𝜒 ) ) )
2	1	imp	⊢ ( ( ∀ 𝑥 ( 𝜓 → 𝜒 ) ∧ ( 𝜑 → ∀ 𝑥 𝜓 ) ) → ( 𝜑 → ∀ 𝑥 𝜒 ) )