Theorem idn3 45800

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 25	. . 3 ⊢ (𝜓 → (𝜒 → 𝜒))
2	1	a1i 11	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜒)))
3	2	dfvd3ir 45778	1 ⊢ (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜒   )

This proof depends on syntax axioms:   → wi 4  (   wvd3 45772

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-3an 1105  df-vd3 45775

This theorem is used by:  suctrALT2VD  46020  en3lplem2VD  46028  exbirVD  46037  exbiriVD  46038  rspsbc2VD  46039  tratrbVD  46045  ssralv2VD  46050  imbi12VD  46057  imbi13VD  46058  truniALTVD  46062  trintALTVD  46064  onfrALTlem2VD  46073