Theorem sylgt 1824

Description: Closed form of sylg 1825. (Contributed by BJ, 2-May-2019.)

Assertion

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

Proof of Theorem sylgt

Step	Hyp	Ref	Expression
1		alim 1813	. 2 ⊢ (∀𝑥(𝜓 → 𝜒) → (∀𝑥𝜓 → ∀𝑥𝜒))
2	1	imim2d 57	1 ⊢ (∀𝑥(𝜓 → 𝜒) → ((𝜑 → ∀𝑥𝜓) → (𝜑 → ∀𝑥𝜒)))

Syntax hints:   → wi 4  ∀wal 1537

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-4 1812

This theorem is referenced by:  bj-sylgt2  34799  bj-alrimg  34800  bj-nexdh  34809  bj-alrim  34875  bj-cbv3ta  34968