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Metamath Proof Explorer

Theorem rexv

Description: An existential quantifier restricted to the universe is unrestricted. (Contributed by NM, 26-Mar-2004)

		Ref	Expression
	Assertion	rexv	$⊢ \exists x \in V φ \leftrightarrow \exists x φ$

Step	Hyp	Ref	Expression
1		df-rex	$⊢ \exists x \in V φ \leftrightarrow \exists x (x \in V \land φ)$
2		vex	$⊢ x \in V$
3	2	biantrur	$⊢ φ \leftrightarrow (x \in V \land φ)$
4	3	exbii	$⊢ \exists x φ \leftrightarrow \exists x (x \in V \land φ)$
5	1 4	bitr4i	$⊢ \exists x \in V φ \leftrightarrow \exists x φ$