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Theorem e201 33860
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e201.1  |-  (. ph ,. ps  ->.  ch ).
e201.2  |-  th
e201.3  |-  (. ph  ->.  ta
).
e201.4  |-  ( ch 
->  ( th  ->  ( ta  ->  et ) ) )
Assertion
Ref Expression
e201  |-  (. ph ,. ps  ->.  et ).

Proof of Theorem e201
StepHypRef Expression
1 e201.1 . 2  |-  (. ph ,. ps  ->.  ch ).
2 e201.2 . . 3  |-  th
32vd01 33796 . 2  |-  (. ph  ->.  th
).
4 e201.3 . 2  |-  (. ph  ->.  ta
).
5 e201.4 . 2  |-  ( ch 
->  ( th  ->  ( ta  ->  et ) ) )
61, 3, 4, 5e211 33856 1  |-  (. ph ,. ps  ->.  et ).
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   (.wvd1 33759   (.wvd2 33767
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 369  df-vd1 33760  df-vd2 33768
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator