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Theorem e23 31790
Description: A virtual deduction elimination rule (see syl10 73). (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 31626 . 2  |-  (. ph ,. ps ,. th  ->.  ch ).
3 e23.2 . 2  |-  (. ph ,. ps ,. th  ->.  ta ).
4 e23.3 . 2  |-  ( ch 
->  ( ta  ->  et ) )
52, 3, 4e33 31769 1  |-  (. ph ,. ps ,. th  ->.  et ).
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   (.wvd2 31592   (.wvd3 31602
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 967  df-vd2 31593  df-vd3 31605
This theorem is referenced by:  e23an  31791  suctrALT2VD  31874  rspsbc2VD  31893  tratrbVD  31899  imbi12VD  31911  imbi13VD  31912
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