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Theorem idn3 28716
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 22 . . 3  |-  ( ps 
->  ( ch  ->  ch ) )
21a1i 11 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  ch ) ) )
32dfvd3ir 28685 1  |-  (. ph ,. ps ,. ch  ->.  ch ).
Colors of variables: wff set class
Syntax hints:    -> wi 4   (.wvd3 28679
This theorem is referenced by:  suctrALT2VD  28948  en3lplem2VD  28956  exbirVD  28965  exbiriVD  28966  rspsbc2VD  28967  tratrbVD  28973  ssralv2VD  28978  imbi12VD  28985  imbi13VD  28986  truniALTVD  28990  trintALTVD  28992  onfrALTlem2VD  29001
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 178  df-an 361  df-3an 938  df-vd3 28682
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