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Theorem e21 28505
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 28372 . 2  |-  (. ph ,. ps  ->.  th ).
4 e21.3 . 2  |-  ( ch 
->  ( th  ->  ta ) )
51, 3, 4e22 28443 1  |-  (. ph ,. ps  ->.  ta ).
Colors of variables: wff set class
Syntax hints:    -> wi 4   (.wvd1 28337   (.wvd2 28346
This theorem is referenced by:  e21an  28506  en3lplem1VD  28619  exbiriVD  28630  syl5impVD  28639  sbcim2gVD  28651  onfrALTlem3VD  28663  onfrALTlem2VD  28665  hbimpgVD  28680  a9e2eqVD  28683  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-vd1 28338  df-vd2 28347
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