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Metamath Proof Explorer

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	$⊢ \exists x (φ \to ψ)$
	Assertion	19.37iv	$⊢ φ \to \exists x ψ$

Proof

Step	Hyp	Ref	Expression
1		19.37iv.1	$⊢ \exists x (φ \to ψ)$
2		19.37imv	$⊢ \exists x (φ \to ψ) \to (φ \to \exists x ψ)$
3	1 2	ax-mp	$⊢ φ \to \exists x ψ$