Theorem elvd 2807

Description: Technical lemma used to shorten proofs. If a proposition is implied by x e. _V (which is true, see vex 2805) 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 2805	. 2 |- x e. _V
2		elvd.1	. 2 |- ( ( ph /\ x e. _V ) -> ps )
3	1, 2	mpan2 425	1 |- ( ph -> ps )

Syntax hints:   -> wi 4   /\ wa 104   e. wcel 2202   _Vcvv 2802

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 1495  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-v 2804

This theorem is referenced by:  omp1eomlem  7292  subrgpropd  14266  imasnopn  15022  pw1nct  16604