Theorem bj-sylggt 36583

Description: Stronger form of sylgt 1820, closer to ax-2 7. (Contributed by BJ, 30-Jul-2025.)

Assertion

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

Proof of Theorem bj-sylggt

Step	Hyp	Ref	Expression
1		alim 1808	. 2 ⊢ (∀𝑥(𝜓 → 𝜒) → (∀𝑥𝜓 → ∀𝑥𝜒))
2	1	imim3i 64	1 ⊢ ((𝜑 → ∀𝑥(𝜓 → 𝜒)) → ((𝜑 → ∀𝑥𝜓) → (𝜑 → ∀𝑥𝜒)))

Syntax hints:   → wi 4  ∀wal 1535

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-4 1807

This theorem is referenced by: (None)