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Theorem e233 28540
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 29-Feb-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e233.1  |-  (. ph ,. ps  ->.  ch ).
e233.2  |-  (. ph ,. ps ,. th  ->.  ta ).
e233.3  |-  (. ph ,. ps ,. th  ->.  et ).
e233.4  |-  ( ch 
->  ( ta  ->  ( et  ->  ze ) ) )
Assertion
Ref Expression
e233  |-  (. ph ,. ps ,. th  ->.  ze ).

Proof of Theorem e233
StepHypRef Expression
1 e233.1 . . . 4  |-  (. ph ,. ps  ->.  ch ).
21dfvd2i 28354 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
3 e233.2 . . . 4  |-  (. ph ,. ps ,. th  ->.  ta ).
43dfvd3i 28361 . . 3  |-  ( ph  ->  ( ps  ->  ( th  ->  ta ) ) )
5 e233.3 . . . 4  |-  (. ph ,. ps ,. th  ->.  et ).
65dfvd3i 28361 . . 3  |-  ( ph  ->  ( ps  ->  ( th  ->  et ) ) )
7 e233.4 . . . 4  |-  ( ch 
->  ( ta  ->  ( et  ->  ze ) ) )
87idi 2 . . 3  |-  ( ch 
->  ( ta  ->  ( et  ->  ze ) ) )
92, 4, 6, 8ee233 28281 . 2  |-  ( ph  ->  ( ps  ->  ( th  ->  ze ) ) )
109dfvd3ir 28362 1  |-  (. ph ,. ps ,. th  ->.  ze ).
Colors of variables: wff set class
Syntax hints:    -> wi 4   (.wvd2 28346   (.wvd3 28356
This theorem is referenced by:  truniALTVD  28654  onfrALTlem2VD  28665
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 28347  df-vd3 28359
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