Theorem sylgt 1854

Description: Closed form of sylg 1855. (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 1842	. 2 ⊢ (∀𝑥(𝜓 → 𝜒) → (∀𝑥𝜓 → ∀𝑥𝜒))
2	1	imim2d 58	1 ⊢ (∀𝑥(𝜓 → 𝜒) → ((𝜑 → ∀𝑥𝜓) → (𝜑 → ∀𝑥𝜒)))

This proof depends on syntax axioms:   → wi 4  ∀wal 1567

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-4 1841

This theorem is used by:  bj-alrimg  37616  bj-sylgt2  37617  bj-nexdh  37618  bj-alrim  37728  bj-cbv3ta  37831