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Theorem e112 36477
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e112.1  |-  (. ph  ->.  ps
).
e112.2  |-  (. ph  ->.  ch
).
e112.3  |-  (. ph ,. th  ->.  ta ).
e112.4  |-  ( ps 
->  ( ch  ->  ( ta  ->  et ) ) )
Assertion
Ref Expression
e112  |-  (. ph ,. th  ->.  et ).

Proof of Theorem e112
StepHypRef Expression
1 e112.1 . . 3  |-  (. ph  ->.  ps
).
21vd12 36423 . 2  |-  (. ph ,. th  ->.  ps ).
3 e112.2 . . 3  |-  (. ph  ->.  ch
).
43vd12 36423 . 2  |-  (. ph ,. th  ->.  ch ).
5 e112.3 . 2  |-  (. ph ,. th  ->.  ta ).
6 e112.4 . 2  |-  ( ps 
->  ( ch  ->  ( ta  ->  et ) ) )
72, 4, 5, 6e222 36459 1  |-  (. ph ,. th  ->.  et ).
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   (.wvd1 36383   (.wvd2 36391
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 187  df-an 371  df-vd1 36384  df-vd2 36392
This theorem is referenced by:  e012  36490  e102  36492
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