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Theorem e100 28759
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e100.1  |-  (. ph  ->.  ps
).
e100.2  |-  ch
e100.3  |-  th
e100.4  |-  ( ps 
->  ( ch  ->  ( th  ->  ta ) ) )
Assertion
Ref Expression
e100  |-  (. ph  ->.  ta
).

Proof of Theorem e100
StepHypRef Expression
1 e100.1 . 2  |-  (. ph  ->.  ps
).
2 e100.2 . . 3  |-  ch
32vd01 28674 . 2  |-  (. ph  ->.  ch
).
4 e100.3 . . 3  |-  th
54vd01 28674 . 2  |-  (. ph  ->.  th
).
6 e100.4 . 2  |-  ( ps 
->  ( ch  ->  ( th  ->  ta ) ) )
71, 3, 5, 6e111 28751 1  |-  (. ph  ->.  ta
).
Colors of variables: wff set class
Syntax hints:    -> wi 4   (.wvd1 28636
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-vd1 28637
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