Theorem bj-sylggt 37238

Description: Stronger form of sylgt 1855, 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 1843	. 2 ⊢ (∀𝑥(𝜓 → 𝜒) → (∀𝑥𝜓 → ∀𝑥𝜒))
2	1	imim3i 65	1 ⊢ ((𝜑 → ∀𝑥(𝜓 → 𝜒)) → ((𝜑 → ∀𝑥𝜓) → (𝜑 → ∀𝑥𝜒)))

This proof depends on syntax axioms:   → wi 4  ∀wal 1568

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-4 1842

This theorem is used by: (None)