Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  e202 Unicode version

Theorem e202 28411
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e202.1  |-  (. ph ,. ps  ->.  ch ).
e202.2  |-  th
e202.3  |-  (. ph ,. ps  ->.  ta ).
e202.4  |-  ( ch 
->  ( th  ->  ( ta  ->  et ) ) )
Assertion
Ref Expression
e202  |-  (. ph ,. ps  ->.  et ).

Proof of Theorem e202
StepHypRef Expression
1 e202.1 . 2  |-  (. ph ,. ps  ->.  ch ).
2 e202.2 . . 3  |-  th
32vd02 28370 . 2  |-  (. ph ,. ps  ->.  th ).
4 e202.3 . 2  |-  (. ph ,. ps  ->.  ta ).
5 e202.4 . 2  |-  ( ch 
->  ( th  ->  ( ta  ->  et ) ) )
61, 3, 4, 5e222 28408 1  |-  (. ph ,. ps  ->.  et ).
Colors of variables: wff set class
Syntax hints:    -> wi 4   (.wvd2 28346
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-vd2 28347
  Copyright terms: Public domain W3C validator