Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  e120 Unicode version

Theorem e120 28435
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 10-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e120.1  |-  (. ph  ->.  ps
).
e120.2  |-  (. ph ,. ch  ->.  th ).
e120.3  |-  ta
e120.4  |-  ( ps 
->  ( th  ->  ( ta  ->  et ) ) )
Assertion
Ref Expression
e120  |-  (. ph ,. ch  ->.  et ).

Proof of Theorem e120
StepHypRef Expression
1 e120.1 . . 3  |-  (. ph  ->.  ps
).
21vd12 28372 . 2  |-  (. ph ,. ch  ->.  ps ).
3 e120.2 . 2  |-  (. ph ,. ch  ->.  th ).
4 e120.3 . 2  |-  ta
5 e120.4 . 2  |-  ( ps 
->  ( th  ->  ( ta  ->  et ) ) )
62, 3, 4, 5e220 28409 1  |-  (. ph ,. ch  ->.  et ).
Colors of variables: wff set class
Syntax hints:    -> wi 4   (.wvd1 28337   (.wvd2 28346
This theorem is referenced by:  pwtrrVD  28600
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 28338  df-vd2 28347
  Copyright terms: Public domain W3C validator