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Theorem e102 28441
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e102.1  |-  (. ph  ->.  ps
).
e102.2  |-  ch
e102.3  |-  (. ph ,. th  ->.  ta ).
e102.4  |-  ( ps 
->  ( ch  ->  ( ta  ->  et ) ) )
Assertion
Ref Expression
e102  |-  (. ph ,. th  ->.  et ).

Proof of Theorem e102
StepHypRef Expression
1 e102.1 . 2  |-  (. ph  ->.  ps
).
2 e102.2 . . 3  |-  ch
32vd01 28369 . 2  |-  (. ph  ->.  ch
).
4 e102.3 . 2  |-  (. ph ,. th  ->.  ta ).
5 e102.4 . 2  |-  ( ps 
->  ( ch  ->  ( ta  ->  et ) ) )
61, 3, 4, 5e112 28426 1  |-  (. ph ,. th  ->.  et ).
Colors of variables: wff set class
Syntax hints:    -> wi 4   (.wvd1 28337   (.wvd2 28346
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-an 360  df-vd1 28338  df-vd2 28347
  Copyright terms: Public domain W3C validator