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	$$⊢\left(x\in \mathrm{V}\wedge y\in \mathrm{V}\right)\to \phi$$
Assertion	el2v	$$⊢\phi$$

Proof

Step	Hyp	Ref	Expression
1		el2v.1	$$⊢\left(x\in \mathrm{V}\wedge y\in \mathrm{V}\right)\to \phi$$
2		vex	$$⊢x\in \mathrm{V}$$
3		vex	$$⊢y\in \mathrm{V}$$
4	2 3 1	mp2an	$$⊢\phi$$