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Theorem idn3 43361
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 43339 1 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜒   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd3 43333
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 206  df-an 397  df-3an 1089  df-vd3 43336
This theorem is referenced by:  suctrALT2VD  43582  en3lplem2VD  43590  exbirVD  43599  exbiriVD  43600  rspsbc2VD  43601  tratrbVD  43607  ssralv2VD  43612  imbi12VD  43619  imbi13VD  43620  truniALTVD  43624  trintALTVD  43626  onfrALTlem2VD  43635
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