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Theorem e211 36447
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e211.1  |-  (. ph ,. ps  ->.  ch ).
e211.2  |-  (. ph  ->.  th
).
e211.3  |-  (. ph  ->.  ta
).
e211.4  |-  ( ch 
->  ( th  ->  ( ta  ->  et ) ) )
Assertion
Ref Expression
e211  |-  (. ph ,. ps  ->.  et ).

Proof of Theorem e211
StepHypRef Expression
1 e211.1 . 2  |-  (. ph ,. ps  ->.  ch ).
2 e211.2 . . 3  |-  (. ph  ->.  th
).
32vd12 36390 . 2  |-  (. ph ,. ps  ->.  th ).
4 e211.3 . . 3  |-  (. ph  ->.  ta
).
54vd12 36390 . 2  |-  (. ph ,. ps  ->.  ta ).
6 e211.4 . 2  |-  ( ch 
->  ( th  ->  ( ta  ->  et ) ) )
71, 3, 5, 6e222 36426 1  |-  (. ph ,. ps  ->.  et ).
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   (.wvd1 36350   (.wvd2 36358
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 36351  df-vd2 36359
This theorem is referenced by:  e210  36449  e201  36451
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