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Theorem e223 28469
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 12-Dec-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e223.1  |-  (. ph ,. ps  ->.  ch ).
e223.2  |-  (. ph ,. ps  ->.  th ).
e223.3  |-  (. ph ,. ps ,. ta  ->.  et ).
e223.4  |-  ( ch 
->  ( th  ->  ( et  ->  ze ) ) )
Assertion
Ref Expression
e223  |-  (. ph ,. ps ,. ta  ->.  ze ).

Proof of Theorem e223
StepHypRef Expression
1 e223.1 . . . . 5  |-  (. ph ,. ps  ->.  ch ).
21in2 28439 . . . 4  |-  (. ph  ->.  ( ps  ->  ch ) ).
32in1 28395 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
4 e223.2 . . . . 5  |-  (. ph ,. ps  ->.  th ).
54in2 28439 . . . 4  |-  (. ph  ->.  ( ps  ->  th ) ).
65in1 28395 . . 3  |-  ( ph  ->  ( ps  ->  th )
)
7 e223.3 . . . . . 6  |-  (. ph ,. ps ,. ta  ->.  et ).
87in3 28443 . . . . 5  |-  (. ph ,. ps  ->.  ( ta  ->  et ) ).
98in2 28439 . . . 4  |-  (. ph  ->.  ( ps  ->  ( ta  ->  et ) ) ).
109in1 28395 . . 3  |-  ( ph  ->  ( ps  ->  ( ta  ->  et ) ) )
11 e223.4 . . 3  |-  ( ch 
->  ( th  ->  ( et  ->  ze ) ) )
123, 6, 10, 11ee223 28468 . 2  |-  ( ph  ->  ( ps  ->  ( ta  ->  ze ) ) )
1312dfvd3ir 28418 1  |-  (. ph ,. ps ,. ta  ->.  ze ).
Colors of variables: wff set class
Syntax hints:    -> wi 4   (.wvd2 28402   (.wvd3 28412
This theorem is referenced by:  tratrbVD  28710
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-vd1 28394  df-vd2 28403  df-vd3 28415
  Copyright terms: Public domain W3C validator