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 e. _V /\ y e. _V ) -> ph )
Assertion el2v
|- ph

Proof

Step Hyp Ref Expression
1 el2v.1
 |-  ( ( x e. _V /\ y e. _V ) -> ph )
2 vex
 |-  x e. _V
3 vex
 |-  y e. _V
4 2 3 1 mp2an
 |-  ph