Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  e121 Unicode version

Theorem e121 28733
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e121.1  |-  (. ph  ->.  ps
).
e121.2  |-  (. ph ,. ch  ->.  th ).
e121.3  |-  (. ph  ->.  ta
).
e121.4  |-  ( ps 
->  ( th  ->  ( ta  ->  et ) ) )
Assertion
Ref Expression
e121  |-  (. ph ,. ch  ->.  et ).

Proof of Theorem e121
StepHypRef Expression
1 e121.1 . . 3  |-  (. ph  ->.  ps
).
21vd12 28677 . 2  |-  (. ph ,. ch  ->.  ps ).
3 e121.2 . 2  |-  (. ph ,. ch  ->.  th ).
4 e121.3 . . 3  |-  (. ph  ->.  ta
).
54vd12 28677 . 2  |-  (. ph ,. ch  ->.  ta ).
6 e121.4 . 2  |-  ( ps 
->  ( th  ->  ( ta  ->  et ) ) )
72, 3, 5, 6e222 28713 1  |-  (. ph ,. ch  ->.  et ).
Colors of variables: wff set class
Syntax hints:    -> wi 4   (.wvd1 28636   (.wvd2 28645
This theorem is referenced by:  e021  28742  tratrbVD  28953
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 177  df-an 360  df-vd1 28637  df-vd2 28646
  Copyright terms: Public domain W3C validator