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Theorem e13 28201
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 13-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e13.1  |-  (. ph  ->.  ps
).
e13.2  |-  (. ph ,. ch ,. th  ->.  ta ).
e13.3  |-  ( ps 
->  ( ta  ->  et ) )
Assertion
Ref Expression
e13  |-  (. ph ,. ch ,. th  ->.  et ).

Proof of Theorem e13
StepHypRef Expression
1 e13.1 . . 3  |-  (. ph  ->.  ps
).
21vd13 28043 . 2  |-  (. ph ,. ch ,. th  ->.  ps ).
3 e13.2 . 2  |-  (. ph ,. ch ,. th  ->.  ta ).
4 e13.3 . 2  |-  ( ps 
->  ( ta  ->  et ) )
52, 3, 4e33 28187 1  |-  (. ph ,. ch ,. th  ->.  et ).
Colors of variables: wff set class
Syntax hints:    -> wi 4   (.wvd1 28001   (.wvd3 28020
This theorem is referenced by:  e13an  28202  en3lplem2VD  28297  rspsbc2VD  28308  ssralv2VD  28319  imbi12VD  28326  imbi13VD  28327  truniALTVD  28331
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-vd1 28002  df-vd3 28023
  Copyright terms: Public domain W3C validator