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

Theorem e23 28941
Description: A virtual deduction elimination rule. (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 28777 . 2  |-  (. ph ,. ps ,. th  ->.  ch ).
3 e23.2 . 2  |-  (. ph ,. ps ,. th  ->.  ta ).
4 e23.3 . 2  |-  ( ch 
->  ( ta  ->  et ) )
52, 3, 4e33 28920 1  |-  (. ph ,. ps ,. th  ->.  et ).
Colors of variables: wff set class
Syntax hints:    -> wi 4   (.wvd2 28743   (.wvd3 28753
This theorem is referenced by:  e23an  28942  suctrALT2VD  29022  rspsbc2VD  29041  tratrbVD  29047  imbi12VD  29059  imbi13VD  29060
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 179  df-an 362  df-3an 939  df-vd2 28744  df-vd3 28756
  Copyright terms: Public domain W3C validator