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Theorem e01 36973
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 36879 . 2  |-  (. ps  ->.  ph ).
3 e01.2 . 2  |-  (. ps  ->.  ch
).
4 e01.3 . 2  |-  ( ph  ->  ( ch  ->  th )
)
52, 3, 4e11 36970 1  |-  (. ps  ->.  th
).
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   (.wvd1 36842
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 36843
This theorem is referenced by:  e01an  36974  trsspwALT  37111  sspwtr  37114  pwtrVD  37125  pwtrrVD  37126  snssiALTVD  37128  snelpwrVD  37132  sstrALT2VD  37135  suctrALT2VD  37137  3impexpVD  37157  ax6e2eqVD  37209  ax6e2ndVD  37210  2sb5ndVD  37212  vk15.4jVD  37216
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