Theorem el2v 2779

Description: If a proposition is implied by x e. _V and y e. _V (which is true, see vex 2776), then it is true. (Contributed by Peter Mazsa, 13-Oct-2018.)

Hypothesis

Ref	Expression
el2v.1	|- ( ( x e. _V /\ y e. _V ) -> ph )

Assertion

Ref	Expression
el2v	|- ph

Proof of Theorem el2v

Step	Hyp	Ref	Expression
1		vex 2776	. 2 |- x e. _V
2		vex 2776	. 2 |- y e. _V
3		el2v.1	. 2 |- ( ( x e. _V /\ y e. _V ) -> ph )
4	1, 2, 3	mp2an 426	1 |- ph

Syntax hints:   -> wi 4   /\ wa 104   e. wcel 2177   _Vcvv 2773

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1471  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-ext 2188

This theorem depends on definitions:  df-bi 117  df-sb 1787  df-clab 2193  df-cleq 2199  df-clel 2202  df-v 2775

This theorem is referenced by: (None)