Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  e23 Structured version   Unicode version

Theorem e23 33946
Description: A virtual deduction elimination rule (see syl10 73). (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e23.1  |-  (. ph ,. ps  ->.  ch ).
e23.2  |-  (. ph ,. ps ,. th  ->.  ta ).
e23.3  |-  ( ch 
->  ( ta  ->  et ) )
Assertion
Ref Expression
e23  |-  (. ph ,. ps ,. th  ->.  et ).

Proof of Theorem e23
StepHypRef Expression
1 e23.1 . . 3  |-  (. ph ,. ps  ->.  ch ).
21vd23 33782 . 2  |-  (. ph ,. ps ,. th  ->.  ch ).
3 e23.2 . 2  |-  (. ph ,. ps ,. th  ->.  ta ).
4 e23.3 . 2  |-  ( ch 
->  ( ta  ->  et ) )
52, 3, 4e33 33925 1  |-  (. ph ,. ps ,. th  ->.  et ).
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   (.wvd2 33748   (.wvd3 33758
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 369  df-3an 973  df-vd2 33749  df-vd3 33761
This theorem is referenced by:  e23an  33947  suctrALT2VD  34036  rspsbc2VD  34055  tratrbVD  34062  imbi12VD  34074  imbi13VD  34075
  Copyright terms: Public domain W3C validator