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Theorem e31 28206
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 13-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e31.1  |-  (. ph ,. ps ,. ch  ->.  th ).
e31.2  |-  (. ph  ->.  ta
).
e31.3  |-  ( th 
->  ( ta  ->  et ) )
Assertion
Ref Expression
e31  |-  (. ph ,. ps ,. ch  ->.  et ).

Proof of Theorem e31
StepHypRef Expression
1 e31.1 . 2  |-  (. ph ,. ps ,. ch  ->.  th ).
2 e31.2 . . 3  |-  (. ph  ->.  ta
).
32vd13 28045 . 2  |-  (. ph ,. ps ,. ch  ->.  ta ).
4 e31.3 . 2  |-  ( th 
->  ( ta  ->  et ) )
51, 3, 4e33 28189 1  |-  (. ph ,. ps ,. ch  ->.  et ).
Colors of variables: wff set class
Syntax hints:    -> wi 4   (.wvd1 28003   (.wvd3 28022
This theorem is referenced by:  e31an  28208  trintALTVD  28335
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 28004  df-vd3 28025
  Copyright terms: Public domain W3C validator