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Theorem e01 31716
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 31622 . 2  |-  (. ps  ->.  ph ).
3 e01.2 . 2  |-  (. ps  ->.  ch
).
4 e01.3 . 2  |-  ( ph  ->  ( ch  ->  th )
)
52, 3, 4e11 31713 1  |-  (. ps  ->.  th
).
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   (.wvd1 31585
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 185  df-vd1 31586
This theorem is referenced by:  e01an  31717  trsspwALT  31855  sspwtr  31858  pwtrVD  31863  pwtrrVD  31864  snssiALTVD  31866  snelpwrVD  31870  sstrALT2VD  31873  suctrALT2VD  31875  3impexpVD  31895  ax6e2eqVD  31946  ax6e2ndVD  31947  2sb5ndVD  31949  vk15.4jVD  31953
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