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Metamath Proof Explorer

Theorem alequexv

Description: Version of equs4v with its consequence simplified by exsimpr . (Contributed by BJ, 9-Nov-2021)

		Ref	Expression
	Assertion	alequexv	$⊢ \forall x (x = y \to φ) \to \exists x φ$

Step	Hyp	Ref	Expression
1		ax6ev	$⊢ \exists x x = y$
2		exim	$⊢ \forall x (x = y \to φ) \to (\exists x x = y \to \exists x φ)$
3	1 2	mpi	$⊢ \forall x (x = y \to φ) \to \exists x φ$