Theorem elv 2626

Description: Technical lemma used to shorten proofs. If a proposition is implied by x e. _V (which is true, see vex 2625), then it is true. (Contributed by Peter Mazsa, 13-Oct-2018.)

Hypothesis

Ref	Expression
elv.1	|- ( x e. _V -> ph )

Assertion

Ref	Expression
elv	|- ph

Proof of Theorem elv

Step	Hyp	Ref	Expression
1		vex 2625	. 2 |- x e. _V
2		elv.1	. 2 |- ( x e. _V -> ph )
3	1, 2	ax-mp 7	1 |- ph

Syntax hints:   -> wi 4   e. wcel 1439   _Vcvv 2622

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 1382  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-ext 2071

This theorem depends on definitions:  df-bi 116  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-v 2624

This theorem is referenced by:  disjxp1  6017  ixpiinm  6497  ixpsnf1o  6509  iunfidisj  6711  fsum2dlemstep  10891  fsumcnv  10894  fisumcom2  10895  fsumconst  10911  modfsummodlemstep  10914  fsumabs  10922  topnfn  11720  iuncld  11878