This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem el2v

Description: If a proposition is implied by x e.V and y e. V (which is true, see vex ), then it is true. (Contributed by Peter Mazsa, 13-Oct-2018)

		Ref	Expression
	Hypothesis	el2v.1	$⊢ (x \in V \land y \in V) \to φ$
	Assertion	el2v	$⊢ φ$

Proof

Step	Hyp	Ref	Expression
1		el2v.1	$⊢ (x \in V \land y \in V) \to φ$
2		vex	$⊢ x \in V$
3		vex	$⊢ y \in V$
4	2 3 1	mp2an	$⊢ φ$