Theorem 19.37iv

Description: Inference associated with 19.37v . (Contributed by NM, 5-Aug-1993) Remove dependency on ax-6 . (Revised by Rohan Ridenour, 15-Apr-2022)

	Ref	Expression
Hypothesis	19.37iv.1	⊢ ∃ 𝑥 ( 𝜑 → 𝜓 )
Assertion	19.37iv	⊢ ( 𝜑 → ∃ 𝑥 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		19.37iv.1	⊢ ∃ 𝑥 ( 𝜑 → 𝜓 )
2		19.37imv	⊢ ( ∃ 𝑥 ( 𝜑 → 𝜓 ) → ( 𝜑 → ∃ 𝑥 𝜓 ) )
3	1 2	ax-mp	⊢ ( 𝜑 → ∃ 𝑥 𝜓 )