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Theorem e33 28846
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e33.1  |-  (. ph ,. ps ,. ch  ->.  th ).
e33.2  |-  (. ph ,. ps ,. ch  ->.  ta ).
e33.3  |-  ( th 
->  ( ta  ->  et ) )
Assertion
Ref Expression
e33  |-  (. ph ,. ps ,. ch  ->.  et ).

Proof of Theorem e33
StepHypRef Expression
1 e33.1 . 2  |-  (. ph ,. ps ,. ch  ->.  th ).
2 e33.2 . 2  |-  (. ph ,. ps ,. ch  ->.  ta ).
3 e33.3 . . 3  |-  ( th 
->  ( ta  ->  et ) )
43a1i 11 . 2  |-  ( th 
->  ( th  ->  ( ta  ->  et ) ) )
51, 1, 2, 4e333 28845 1  |-  (. ph ,. ps ,. ch  ->.  et ).
Colors of variables: wff set class
Syntax hints:    -> wi 4   (.wvd3 28679
This theorem is referenced by:  e33an  28847  e3  28849  e03  28852  e30  28856  e13  28860  e31  28863  e23  28867  e32  28870  truniALTVD  28990  trintALTVD  28992  onfrALTlem2VD  29001
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-vd3 28682
  Copyright terms: Public domain W3C validator