Theorem 19.36iv

Description: Inference associated with 19.36v . Version of 19.36i with a disjoint variable condition. (Contributed by NM, 5-Aug-1993) Reduce dependencies on axioms. (Revised by Wolf Lammen, 17-Jan-2020) Remove dependency on ax-6 . (Revised by Rohan Ridenour, 15-Apr-2022)

	Ref	Expression
Hypothesis	19.36iv.1	⊢ ∃ 𝑥 ( 𝜑 → 𝜓 )
Assertion	19.36iv	⊢ ( ∀ 𝑥 𝜑 → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		19.36iv.1	⊢ ∃ 𝑥 ( 𝜑 → 𝜓 )
2		19.36imv	⊢ ( ∃ 𝑥 ( 𝜑 → 𝜓 ) → ( ∀ 𝑥 𝜑 → 𝜓 ) )
3	1 2	ax-mp	⊢ ( ∀ 𝑥 𝜑 → 𝜓 )