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Metamath Proof Explorer

Theorem ax5ea

Description: If a formula holds for some value of a variable not occurring in it, then it holds for all values of that variable. (Contributed by BJ, 28-Dec-2020)

		Ref	Expression
	Assertion	ax5ea	$⊢ \exists x φ \to \forall x φ$

Proof

Step	Hyp	Ref	Expression
1		ax5e	$⊢ \exists x φ \to φ$
2		ax-5	$⊢ φ \to \forall x φ$
3	1 2	syl	$⊢ \exists x φ \to \forall x φ$