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Theorem e02 28470
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 14-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e02.1  |-  ph
e02.2  |-  (. ps ,. ch  ->.  th ).
e02.3  |-  ( ph  ->  ( th  ->  ta ) )
Assertion
Ref Expression
e02  |-  (. ps ,. ch  ->.  ta ).

Proof of Theorem e02
StepHypRef Expression
1 e02.1 . . 3  |-  ph
21vd02 28370 . 2  |-  (. ps ,. ch  ->.  ph ).
3 e02.2 . 2  |-  (. ps ,. ch  ->.  th ).
4 e02.3 . 2  |-  ( ph  ->  ( th  ->  ta ) )
52, 3, 4e22 28443 1  |-  (. ps ,. ch  ->.  ta ).
Colors of variables: wff set class
Syntax hints:    -> wi 4   (.wvd2 28346
This theorem is referenced by:  e02an  28471  onfrALTlem3VD  28663  vk15.4jVD  28690
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-vd2 28347
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