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Theorem e211 28429
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 28372 . 2  |-  (. ph ,. ps  ->.  th ).
4 e211.3 . . 3  |-  (. ph  ->.  ta
).
54vd12 28372 . 2  |-  (. ph ,. ps  ->.  ta ).
6 e211.4 . 2  |-  ( ch 
->  ( th  ->  ( ta  ->  et ) ) )
71, 3, 5, 6e222 28408 1  |-  (. ph ,. ps  ->.  et ).
Colors of variables: wff set class
Syntax hints:    -> wi 4   (.wvd1 28337   (.wvd2 28346
This theorem is referenced by:  e210  28431  e201  28433
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-vd1 28338  df-vd2 28347
  Copyright terms: Public domain W3C validator