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Theorem e122 28730
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e122.1  |-  (. ph  ->.  ps
).
e122.2  |-  (. ph ,. ch  ->.  th ).
e122.3  |-  (. ph ,. ch  ->.  ta ).
e122.4  |-  ( ps 
->  ( th  ->  ( ta  ->  et ) ) )
Assertion
Ref Expression
e122  |-  (. ph ,. ch  ->.  et ).

Proof of Theorem e122
StepHypRef Expression
1 e122.1 . . 3  |-  (. ph  ->.  ps
).
21vd12 28677 . 2  |-  (. ph ,. ch  ->.  ps ).
3 e122.2 . 2  |-  (. ph ,. ch  ->.  th ).
4 e122.3 . 2  |-  (. ph ,. ch  ->.  ta ).
5 e122.4 . 2  |-  ( ps 
->  ( th  ->  ( ta  ->  et ) ) )
62, 3, 4, 5e222 28713 1  |-  (. ph ,. ch  ->.  et ).
Colors of variables: wff set class
Syntax hints:    -> wi 4   (.wvd1 28636   (.wvd2 28645
This theorem is referenced by:  tratrbVD  28953
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-vd1 28637  df-vd2 28646
  Copyright terms: Public domain W3C validator