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Theorem e21 37117
Description: A virtual deduction elimination rule (see syl6ci 67). (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 36979 . 2  |-  (. ph ,. ps  ->.  th ).
4 e21.3 . 2  |-  ( ch 
->  ( th  ->  ta ) )
51, 3, 4e22 37050 1  |-  (. ph ,. ps  ->.  ta ).
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   (.wvd1 36939   (.wvd2 36947
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 189  df-an 373  df-vd1 36940  df-vd2 36948
This theorem is referenced by:  e21an  37118  en3lplem1VD  37239  exbiriVD  37250  syl5impVD  37260  sbcim2gVD  37272  onfrALTlem3VD  37284  onfrALTlem2VD  37286  hbimpgVD  37301  ax6e2eqVD  37304  vk15.4jVD  37311
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