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Theorem idn3 31639
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 31608 1  |-  (. ph ,. ps ,. ch  ->.  ch ).
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   (.wvd3 31602
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 371  df-3an 967  df-vd3 31605
This theorem is referenced by:  suctrALT2VD  31874  en3lplem2VD  31882  exbirVD  31891  exbiriVD  31892  rspsbc2VD  31893  tratrbVD  31899  ssralv2VD  31904  imbi12VD  31911  imbi13VD  31912  truniALTVD  31916  trintALTVD  31918  onfrALTlem2VD  31927
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