Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  idn3 Unicode version

Theorem idn3 28387
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 21 . . 3  |-  ( ps 
->  ( ch  ->  ch ) )
21a1i 10 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  ch ) ) )
32dfvd3ir 28362 1  |-  (. ph ,. ps ,. ch  ->.  ch ).
Colors of variables: wff set class
Syntax hints:    -> wi 4   (.wvd3 28356
This theorem is referenced by:  suctrALT2VD  28612  en3lplem2VD  28620  exbirVD  28629  exbiriVD  28630  rspsbc2VD  28631  tratrbVD  28637  ssralv2VD  28642  imbi12VD  28649  imbi13VD  28650  truniALTVD  28654  trintALTVD  28656  onfrALTlem2VD  28665
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-3an 936  df-vd3 28359
  Copyright terms: Public domain W3C validator