Theorem el2v 2827

Description: If a proposition is implied by x e. _V and y e. _V (which is true, see vex 2824), 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 2824	. 2 |- x e. _V
2		vex 2824	. 2 |- y e. _V
3		el2v.1	. 2 |- ( ( x e. _V /\ y e. _V ) -> ph )
4	1, 2, 3	mp2an 430	1 |- ph

This proof depends on syntax axioms:   -> wi 4   /\ wa 104   e. wcel 2209   _Vcvv 2821

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1500  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-ext 2220

This proof depends on definitions:  df-bi 117  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-v 2823

This theorem is used by:  en2prde  7539  upgr1een  16365