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Theorem e110 28753
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e110.1  |-  (. ph  ->.  ps
).
e110.2  |-  (. ph  ->.  ch
).
e110.3  |-  th
e110.4  |-  ( ps 
->  ( ch  ->  ( th  ->  ta ) ) )
Assertion
Ref Expression
e110  |-  (. ph  ->.  ta
).

Proof of Theorem e110
StepHypRef Expression
1 e110.1 . 2  |-  (. ph  ->.  ps
).
2 e110.2 . 2  |-  (. ph  ->.  ch
).
3 e110.3 . . 3  |-  th
43vd01 28674 . 2  |-  (. ph  ->.  th
).
5 e110.4 . 2  |-  ( ps 
->  ( ch  ->  ( th  ->  ta ) ) )
61, 2, 4, 5e111 28751 1  |-  (. ph  ->.  ta
).
Colors of variables: wff set class
Syntax hints:    -> wi 4   (.wvd1 28636
This theorem is referenced by:  2uasbanhVD  29003
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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