Theorem sylgt

Description: Closed form of sylg . (Contributed by BJ, 2-May-2019)

	Ref	Expression
Assertion	sylgt	⊢ ( ∀ 𝑥 ( 𝜓 → 𝜒 ) → ( ( 𝜑 → ∀ 𝑥 𝜓 ) → ( 𝜑 → ∀ 𝑥 𝜒 ) ) )

Proof

Step	Hyp	Ref	Expression
1		alim	⊢ ( ∀ 𝑥 ( 𝜓 → 𝜒 ) → ( ∀ 𝑥 𝜓 → ∀ 𝑥 𝜒 ) )
2	1	imim2d	⊢ ( ∀ 𝑥 ( 𝜓 → 𝜒 ) → ( ( 𝜑 → ∀ 𝑥 𝜓 ) → ( 𝜑 → ∀ 𝑥 𝜒 ) ) )