Theorem bj-sylget

Description: Dual statement of sylgt . Closed form of bj-sylge . (Contributed by BJ, 2-May-2019)

	Ref	Expression
Assertion	bj-sylget	⊢ ( ∀ 𝑥 ( 𝜒 → 𝜑 ) → ( ( ∃ 𝑥 𝜑 → 𝜓 ) → ( ∃ 𝑥 𝜒 → 𝜓 ) ) )

Proof

Step	Hyp	Ref	Expression
1		exim	⊢ ( ∀ 𝑥 ( 𝜒 → 𝜑 ) → ( ∃ 𝑥 𝜒 → ∃ 𝑥 𝜑 ) )
2	1	imim1d	⊢ ( ∀ 𝑥 ( 𝜒 → 𝜑 ) → ( ( ∃ 𝑥 𝜑 → 𝜓 ) → ( ∃ 𝑥 𝜒 → 𝜓 ) ) )