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Theorem e23 28580
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e23.1  |-  (. ph ,. ps  ->.  ch ).
e23.2  |-  (. ph ,. ps ,. th  ->.  ta ).
e23.3  |-  ( ch 
->  ( ta  ->  et ) )
Assertion
Ref Expression
e23  |-  (. ph ,. ps ,. th  ->.  et ).

Proof of Theorem e23
StepHypRef Expression
1 e23.1 . . 3  |-  (. ph ,. ps  ->.  ch ).
21vd23 28416 . 2  |-  (. ph ,. ps ,. th  ->.  ch ).
3 e23.2 . 2  |-  (. ph ,. ps ,. th  ->.  ta ).
4 e23.3 . 2  |-  ( ch 
->  ( ta  ->  et ) )
52, 3, 4e33 28559 1  |-  (. ph ,. ps ,. th  ->.  et ).
Colors of variables: wff set class
Syntax hints:    -> wi 4   (.wvd2 28382   (.wvd3 28392
This theorem is referenced by:  e23an  28581  suctrALT2VD  28661  rspsbc2VD  28680  tratrbVD  28686  imbi12VD  28698  imbi13VD  28699
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 178  df-an 361  df-3an 938  df-vd2 28383  df-vd3 28395
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