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Theorem e221 28421
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e221.1  |-  (. ph ,. ps  ->.  ch ).
e221.2  |-  (. ph ,. ps  ->.  th ).
e221.3  |-  (. ph  ->.  ta
).
e221.4  |-  ( ch 
->  ( th  ->  ( ta  ->  et ) ) )
Assertion
Ref Expression
e221  |-  (. ph ,. ps  ->.  et ).

Proof of Theorem e221
StepHypRef Expression
1 e221.1 . 2  |-  (. ph ,. ps  ->.  ch ).
2 e221.2 . 2  |-  (. ph ,. ps  ->.  th ).
3 e221.3 . . 3  |-  (. ph  ->.  ta
).
43vd12 28372 . 2  |-  (. ph ,. ps  ->.  ta ).
5 e221.4 . 2  |-  ( ch 
->  ( th  ->  ( ta  ->  et ) ) )
61, 2, 4, 5e222 28408 1  |-  (. ph ,. ps  ->.  et ).
Colors of variables: wff set class
Syntax hints:    -> wi 4   (.wvd1 28337   (.wvd2 28346
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