Theorem idn3 43019

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

Step	Hyp	Ref	Expression
1		idd 24	. . 3 ⊢ (𝜓 → (𝜒 → 𝜒))
2	1	a1i 11	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜒)))
3	2	dfvd3ir 42997	1 ⊢ (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜒   )

Syntax hints:   → wi 4  (   wvd3 42991

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 42994

This theorem is referenced by:  suctrALT2VD  43240  en3lplem2VD  43248  exbirVD  43257  exbiriVD  43258  rspsbc2VD  43259  tratrbVD  43265  ssralv2VD  43270  imbi12VD  43277  imbi13VD  43278  truniALTVD  43282  trintALTVD  43284  onfrALTlem2VD  43293