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Theorem e020 28417
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e020.1  |-  ph
e020.2  |-  (. ps ,. ch  ->.  th ).
e020.3  |-  ta
e020.4  |-  ( ph  ->  ( th  ->  ( ta  ->  et ) ) )
Assertion
Ref Expression
e020  |-  (. ps ,. ch  ->.  et ).

Proof of Theorem e020
StepHypRef Expression
1 e020.1 . . 3  |-  ph
21vd02 28370 . 2  |-  (. ps ,. ch  ->.  ph ).
3 e020.2 . 2  |-  (. ps ,. ch  ->.  th ).
4 e020.3 . . 3  |-  ta
54vd02 28370 . 2  |-  (. ps ,. ch  ->.  ta ).
6 e020.4 . 2  |-  ( ph  ->  ( th  ->  ( ta  ->  et ) ) )
72, 3, 5, 6e222 28408 1  |-  (. ps ,. ch  ->.  et ).
Colors of variables: wff set class
Syntax hints:    -> wi 4   (.wvd2 28346
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-vd2 28347
  Copyright terms: Public domain W3C validator