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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
StepHypRef Expression
1 vex 2625 . 2  |-  x  e. 
_V
2 elv.1 . 2  |-  ( x  e.  _V  ->  ph )
31, 2ax-mp 7 1  |-  ph
Colors of variables: wff set class
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
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