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Theorem e21 28904
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e21.1  |-  (. ph ,. ps  ->.  ch ).
e21.2  |-  (. ph  ->.  th
).
e21.3  |-  ( ch 
->  ( th  ->  ta ) )
Assertion
Ref Expression
e21  |-  (. ph ,. ps  ->.  ta ).

Proof of Theorem e21
StepHypRef Expression
1 e21.1 . 2  |-  (. ph ,. ps  ->.  ch ).
2 e21.2 . . 3  |-  (. ph  ->.  th
).
32vd12 28763 . 2  |-  (. ph ,. ps  ->.  th ).
4 e21.3 . 2  |-  ( ch 
->  ( th  ->  ta ) )
51, 3, 4e22 28834 1  |-  (. ph ,. ps  ->.  ta ).
Colors of variables: wff set class
Syntax hints:    -> wi 4   (.wvd1 28722   (.wvd2 28731
This theorem is referenced by:  e21an  28905  en3lplem1VD  29017  exbiriVD  29028  syl5impVD  29037  sbcim2gVD  29049  onfrALTlem3VD  29061  onfrALTlem2VD  29063  hbimpgVD  29078  a9e2eqVD  29081  vk15.4jVD  29088
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 179  df-an 362  df-vd1 28723  df-vd2 28732
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