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Theorem e01 33871
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 33777 . 2  |-  (. ps  ->.  ph ).
3 e01.2 . 2  |-  (. ps  ->.  ch
).
4 e01.3 . 2  |-  ( ph  ->  ( ch  ->  th )
)
52, 3, 4e11 33868 1  |-  (. ps  ->.  th
).
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   (.wvd1 33740
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 33741
This theorem is referenced by:  e01an  33872  trsspwALT  34010  sspwtr  34013  pwtrVD  34024  pwtrrVD  34025  snssiALTVD  34027  snelpwrVD  34031  sstrALT2VD  34034  suctrALT2VD  34036  3impexpVD  34056  ax6e2eqVD  34108  ax6e2ndVD  34109  2sb5ndVD  34111  vk15.4jVD  34115
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