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Metamath Proof Explorer

Theorem ralv

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

		Ref	Expression
	Assertion	ralv	$⊢ \forall x \in V φ \leftrightarrow \forall x φ$

Step	Hyp	Ref	Expression
1		df-ral	$⊢ \forall x \in V φ \leftrightarrow \forall x (x \in V \to φ)$
2		vex	$⊢ x \in V$
3	2	a1bi	$⊢ φ \leftrightarrow (x \in V \to φ)$
4	3	albii	$⊢ \forall x φ \leftrightarrow \forall x (x \in V \to φ)$
5	1 4	bitr4i	$⊢ \forall x \in V φ \leftrightarrow \forall x φ$