Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  e21 Unicode version

Theorem e21 28819
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e21.1  |-  (. ph ,. ps  ->.  ch ).
e21.2  |-  (. ph  ->.  th
).
e21.3  |-  ( ch 
->  ( th  ->  ta ) )
Assertion
Ref Expression
e21  |-  (. ph ,. ps  ->.  ta ).

Proof of Theorem e21
StepHypRef Expression
1 e21.1 . 2  |-  (. ph ,. ps  ->.  ch ).
2 e21.2 . . 3  |-  (. ph  ->.  th
).
32vd12 28677 . 2  |-  (. ph ,. ps  ->.  th ).
4 e21.3 . 2  |-  ( ch 
->  ( th  ->  ta ) )
51, 3, 4e22 28748 1  |-  (. ph ,. ps  ->.  ta ).
Colors of variables: wff set class
Syntax hints:    -> wi 4   (.wvd1 28636   (.wvd2 28645
This theorem is referenced by:  e21an  28820  en3lplem1VD  28935  exbiriVD  28946  syl5impVD  28955  sbcim2gVD  28967  onfrALTlem3VD  28979  onfrALTlem2VD  28981  hbimpgVD  28996  a9e2eqVD  28999  vk15.4jVD  29006
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