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Theorem e323 28855
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 17-Apr-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e323.1  |-  (. ph ,. ps ,. ch  ->.  th ).
e323.2  |-  (. ph ,. ps  ->.  ta ).
e323.3  |-  (. ph ,. ps ,. ch  ->.  et ).
e323.4  |-  ( th 
->  ( ta  ->  ( et  ->  ze ) ) )
Assertion
Ref Expression
e323  |-  (. ph ,. ps ,. ch  ->.  ze ).

Proof of Theorem e323
StepHypRef Expression
1 e323.1 . . . 4  |-  (. ph ,. ps ,. ch  ->.  th ).
21dfvd3i 28660 . . 3  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
3 e323.2 . . . 4  |-  (. ph ,. ps  ->.  ta ).
43dfvd2i 28653 . . 3  |-  ( ph  ->  ( ps  ->  ta ) )
5 e323.3 . . . 4  |-  (. ph ,. ps ,. ch  ->.  et ).
65dfvd3i 28660 . . 3  |-  ( ph  ->  ( ps  ->  ( ch  ->  et ) ) )
7 e323.4 . . 3  |-  ( th 
->  ( ta  ->  ( et  ->  ze ) ) )
82, 4, 6, 7ee323 28568 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  ze ) ) )
98dfvd3ir 28661 1  |-  (. ph ,. ps ,. ch  ->.  ze ).
Colors of variables: wff set class
Syntax hints:    -> wi 4   (.wvd2 28645   (.wvd3 28655
This theorem is referenced by:  trintALTVD  28972
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 177  df-an 360  df-3an 936  df-vd2 28646  df-vd3 28658
  Copyright terms: Public domain W3C validator