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Theorem idn3 44588
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 44566 1 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜒   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd3 44560
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 207  df-an 396  df-3an 1089  df-vd3 44563
This theorem is referenced by:  suctrALT2VD  44809  en3lplem2VD  44817  exbirVD  44826  exbiriVD  44827  rspsbc2VD  44828  tratrbVD  44834  ssralv2VD  44839  imbi12VD  44846  imbi13VD  44847  truniALTVD  44851  trintALTVD  44853  onfrALTlem2VD  44862
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