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Theorem e101 28450
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e101.1  |-  (. ph  ->.  ps
).
e101.2  |-  ch
e101.3  |-  (. ph  ->.  th
).
e101.4  |-  ( ps 
->  ( ch  ->  ( th  ->  ta ) ) )
Assertion
Ref Expression
e101  |-  (. ph  ->.  ta
).

Proof of Theorem e101
StepHypRef Expression
1 e101.1 . 2  |-  (. ph  ->.  ps
).
2 e101.2 . . 3  |-  ch
32vd01 28369 . 2  |-  (. ph  ->.  ch
).
4 e101.3 . 2  |-  (. ph  ->.  th
).
5 e101.4 . 2  |-  ( ps 
->  ( ch  ->  ( th  ->  ta ) ) )
61, 3, 4, 5e111 28446 1  |-  (. ph  ->.  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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