Theorem bj-sylggt

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

	Ref	Expression
Assertion	bj-sylggt	⊢ ( ( 𝜑 → ∀ 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	imim3i	⊢ ( ( 𝜑 → ∀ 𝑥 ( 𝜓 → 𝜒 ) ) → ( ( 𝜑 → ∀ 𝑥 𝜓 ) → ( 𝜑 → ∀ 𝑥 𝜒 ) ) )