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Theorem idn3 39342
Description: Virtual deduction identity rule for three virtual hypotheses. (Contributed by Alan Sare, 11-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
idn3 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜒   )

Proof of Theorem idn3
StepHypRef Expression
1 idd 24 . . 3 (𝜓 → (𝜒𝜒))
21a1i 11 . 2 (𝜑 → (𝜓 → (𝜒𝜒)))
32dfvd3ir 39311 1 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜒   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd3 39305
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 197  df-an 385  df-3an 1074  df-vd3 39308
This theorem is referenced by:  suctrALT2VD  39570  en3lplem2VD  39578  exbirVD  39587  exbiriVD  39588  rspsbc2VD  39589  tratrbVD  39596  ssralv2VD  39601  imbi12VD  39608  imbi13VD  39609  truniALTVD  39613  trintALTVD  39615  onfrALTlem2VD  39624
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