Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  e012 Structured version   Unicode version

Theorem e012 28705
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e012.1  |-  ph
e012.2  |-  (. ps  ->.  ch
).
e012.3  |-  (. ps ,. th  ->.  ta ).
e012.4  |-  ( ph  ->  ( ch  ->  ( ta  ->  et ) ) )
Assertion
Ref Expression
e012  |-  (. ps ,. th  ->.  et ).

Proof of Theorem e012
StepHypRef Expression
1 e012.1 . . 3  |-  ph
21vd01 28635 . 2  |-  (. ps  ->.  ph ).
3 e012.2 . 2  |-  (. ps  ->.  ch
).
4 e012.3 . 2  |-  (. ps ,. th  ->.  ta ).
5 e012.4 . 2  |-  ( ph  ->  ( ch  ->  ( ta  ->  et ) ) )
62, 3, 4, 5e112 28692 1  |-  (. ps ,. th  ->.  et ).
Colors of variables: wff set class
Syntax hints:    -> wi 4   (.wvd1 28597   (.wvd2 28606
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 178  df-an 361  df-vd1 28598  df-vd2 28607
  Copyright terms: Public domain W3C validator