Theorem elvd 2660

Description: Technical lemma used to shorten proofs. If a proposition is implied by x e. _V (which is true, see vex 2658) and another antecedent, then it is implied by the other antecedent. (Contributed by Peter Mazsa, 23-Oct-2018.)

Hypothesis

Ref	Expression
elvd.1	|- ( ( ph /\ x e. _V ) -> ps )

Assertion

Ref	Expression
elvd	|- ( ph -> ps )

Proof of Theorem elvd

Step	Hyp	Ref	Expression
1		vex 2658	. 2 |- x e. _V
2		elvd.1	. 2 |- ( ( ph /\ x e. _V ) -> ps )
3	1, 2	mpan2 419	1 |- ( ph -> ps )

Syntax hints:   -> wi 4   /\ wa 103   e. wcel 1461   _Vcvv 2655

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1404  ax-gen 1406  ax-ie1 1450  ax-ie2 1451  ax-8 1463  ax-4 1468  ax-17 1487  ax-i9 1491  ax-ial 1495  ax-ext 2095

This theorem depends on definitions:  df-bi 116  df-sb 1717  df-clab 2100  df-cleq 2106  df-clel 2109  df-v 2657

This theorem is referenced by:  omp1eomlem  6929  imasnopn  12304