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Theorem e123 28851
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e123.1  |-  (. ph  ->.  ps
).
e123.2  |-  (. ph ,. ch  ->.  th ).
e123.3  |-  (. ph ,. ch ,. ta  ->.  et ).
e123.4  |-  ( ps 
->  ( th  ->  ( et  ->  ze ) ) )
Assertion
Ref Expression
e123  |-  (. ph ,. ch ,. ta  ->.  ze ).

Proof of Theorem e123
StepHypRef Expression
1 e123.1 . . 3  |-  (. ph  ->.  ps
).
21vd13 28678 . 2  |-  (. ph ,. ch ,. ta  ->.  ps ).
3 e123.2 . . 3  |-  (. ph ,. ch  ->.  th ).
43vd23 28679 . 2  |-  (. ph ,. ch ,. ta  ->.  th ).
5 e123.3 . 2  |-  (. ph ,. ch ,. ta  ->.  et ).
6 e123.4 . 2  |-  ( ps 
->  ( th  ->  ( et  ->  ze ) ) )
72, 4, 5, 6e333 28822 1  |-  (. ph ,. ch ,. ta  ->.  ze ).
Colors of variables: wff set class
Syntax hints:    -> wi 4   (.wvd1 28636   (.wvd2 28645   (.wvd3 28655
This theorem is referenced by:  suctrALT2VD  28928
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 28637  df-vd2 28646  df-vd3 28658
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