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Theorem e010 28456
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e010.1  |-  ph
e010.2  |-  (. ps  ->.  ch
).
e010.3  |-  th
e010.4  |-  ( ph  ->  ( ch  ->  ( th  ->  ta ) ) )
Assertion
Ref Expression
e010  |-  (. ps  ->.  ta
).

Proof of Theorem e010
StepHypRef Expression
1 e010.1 . . 3  |-  ph
21vd01 28369 . 2  |-  (. ps  ->.  ph ).
3 e010.2 . 2  |-  (. ps  ->.  ch
).
4 e010.3 . . 3  |-  th
54vd01 28369 . 2  |-  (. ps  ->.  th
).
6 e010.4 . 2  |-  ( ph  ->  ( ch  ->  ( th  ->  ta ) ) )
72, 3, 5, 6e111 28446 1  |-  (. ps  ->.  ta
).
Colors of variables: wff set class
Syntax hints:    -> wi 4   (.wvd1 28337
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 28338
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