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Theorem idn3 33795
Description: Virtual deduction identity rule for 3 virtual hypotheses. (Contributed by Alan Sare, 11-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
idn3  |-  (. ph ,. ps ,. ch  ->.  ch ).

Proof of Theorem idn3
StepHypRef Expression
1 idd 24 . . 3  |-  ( ps 
->  ( ch  ->  ch ) )
21a1i 11 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  ch ) ) )
32dfvd3ir 33764 1  |-  (. ph ,. ps ,. ch  ->.  ch ).
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   (.wvd3 33758
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 185  df-an 369  df-3an 973  df-vd3 33761
This theorem is referenced by:  suctrALT2VD  34036  en3lplem2VD  34044  exbirVD  34053  exbiriVD  34054  rspsbc2VD  34055  tratrbVD  34062  ssralv2VD  34067  imbi12VD  34074  imbi13VD  34075  truniALTVD  34079  trintALTVD  34081  onfrALTlem2VD  34090
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