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Theorem e121 31691
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e121.1  |-  (. ph  ->.  ps
).
e121.2  |-  (. ph ,. ch  ->.  th ).
e121.3  |-  (. ph  ->.  ta
).
e121.4  |-  ( ps 
->  ( th  ->  ( ta  ->  et ) ) )
Assertion
Ref Expression
e121  |-  (. ph ,. ch  ->.  et ).

Proof of Theorem e121
StepHypRef Expression
1 e121.1 . . 3  |-  (. ph  ->.  ps
).
21vd12 31635 . 2  |-  (. ph ,. ch  ->.  ps ).
3 e121.2 . 2  |-  (. ph ,. ch  ->.  th ).
4 e121.3 . . 3  |-  (. ph  ->.  ta
).
54vd12 31635 . 2  |-  (. ph ,. ch  ->.  ta ).
6 e121.4 . 2  |-  ( ps 
->  ( th  ->  ( ta  ->  et ) ) )
72, 3, 5, 6e222 31671 1  |-  (. ph ,. ch  ->.  et ).
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   (.wvd1 31595   (.wvd2 31603
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 185  df-an 371  df-vd1 31596  df-vd2 31604
This theorem is referenced by:  e021  31700  tratrbVD  31910
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