Theorem 19.36imvOLD

Description: Obsolete version of 19.36imv as of 22-Sep-2024. (Contributed by Rohan Ridenour, 16-Apr-2022) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	19.36imvOLD	⊢ ( ∃ 𝑥 ( 𝜑 → 𝜓 ) → ( ∀ 𝑥 𝜑 → 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		19.35	⊢ ( ∃ 𝑥 ( 𝜑 → 𝜓 ) ↔ ( ∀ 𝑥 𝜑 → ∃ 𝑥 𝜓 ) )
2	1	biimpi	⊢ ( ∃ 𝑥 ( 𝜑 → 𝜓 ) → ( ∀ 𝑥 𝜑 → ∃ 𝑥 𝜓 ) )
3		ax5e	⊢ ( ∃ 𝑥 𝜓 → 𝜓 )
4	2 3	syl6	⊢ ( ∃ 𝑥 ( 𝜑 → 𝜓 ) → ( ∀ 𝑥 𝜑 → 𝜓 ) )