Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  e01 Structured version   Visualization version   Unicode version

Theorem e01 37070
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 25-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e01.1  |-  ph
e01.2  |-  (. ps  ->.  ch
).
e01.3  |-  ( ph  ->  ( ch  ->  th )
)
Assertion
Ref Expression
e01  |-  (. ps  ->.  th
).

Proof of Theorem e01
StepHypRef Expression
1 e01.1 . . 3  |-  ph
21vd01 36976 . 2  |-  (. ps  ->.  ph ).
3 e01.2 . 2  |-  (. ps  ->.  ch
).
4 e01.3 . 2  |-  ( ph  ->  ( ch  ->  th )
)
52, 3, 4e11 37067 1  |-  (. ps  ->.  th
).
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   (.wvd1 36939
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 189  df-vd1 36940
This theorem is referenced by:  e01an  37071  trsspwALT  37206  sspwtr  37209  pwtrVD  37220  pwtrrVD  37221  snssiALTVD  37223  snelpwrVD  37227  sstrALT2VD  37230  suctrALT2VD  37232  3impexpVD  37252  ax6e2eqVD  37304  ax6e2ndVD  37305  2sb5ndVD  37307  vk15.4jVD  37311
  Copyright terms: Public domain W3C validator