Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  e210 Unicode version

Theorem e210 28736
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e210.1  |-  (. ph ,. ps  ->.  ch ).
e210.2  |-  (. ph  ->.  th
).
e210.3  |-  ta
e210.4  |-  ( ch 
->  ( th  ->  ( ta  ->  et ) ) )
Assertion
Ref Expression
e210  |-  (. ph ,. ps  ->.  et ).

Proof of Theorem e210
StepHypRef Expression
1 e210.1 . 2  |-  (. ph ,. ps  ->.  ch ).
2 e210.2 . 2  |-  (. ph  ->.  th
).
3 e210.3 . . 3  |-  ta
43vd01 28674 . 2  |-  (. ph  ->.  ta
).
5 e210.4 . 2  |-  ( ch 
->  ( th  ->  ( ta  ->  et ) ) )
61, 2, 4, 5e211 28734 1  |-  (. ph ,. ps  ->.  et ).
Colors of variables: wff set class
Syntax hints:    -> wi 4   (.wvd1 28636   (.wvd2 28645
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