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Theorem e011 28757
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e011.1  |-  ph
e011.2  |-  (. ps  ->.  ch
).
e011.3  |-  (. ps  ->.  th
).
e011.4  |-  ( ph  ->  ( ch  ->  ( th  ->  ta ) ) )
Assertion
Ref Expression
e011  |-  (. ps  ->.  ta
).

Proof of Theorem e011
StepHypRef Expression
1 e011.1 . . 3  |-  ph
21vd01 28674 . 2  |-  (. ps  ->.  ph ).
3 e011.2 . 2  |-  (. ps  ->.  ch
).
4 e011.3 . 2  |-  (. ps  ->.  th
).
5 e011.4 . 2  |-  ( ph  ->  ( ch  ->  ( th  ->  ta ) ) )
62, 3, 4, 5e111 28751 1  |-  (. ps  ->.  ta
).
Colors of variables: wff set class
Syntax hints:    -> wi 4   (.wvd1 28636
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-vd1 28637
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