Theorem in3 45781

Description: The virtual deduction introduction rule of converting the end virtual hypothesis of 3 virtual hypotheses into an antecedent. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
in3.1	⊢ (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )

Assertion

Ref	Expression
in3	⊢ (   𝜑   ,   𝜓   ▶   (𝜒 → 𝜃)   )

Proof of Theorem in3

Step	Hyp	Ref	Expression
1		in3.1	. . 3 ⊢ (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )
2	1	dfvd3i 45764	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
3	2	dfvd2ir 45758	1 ⊢ (   𝜑   ,   𝜓   ▶   (𝜒 → 𝜃)   )

This proof depends on syntax axioms:   → wi 4  (   wvd2 45749  (   wvd3 45759

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-vd2 45750  df-vd3 45762

This theorem is used by:  e223  45807  suctrALT2VD  46007  en3lplem2VD  46015  exbirVD  46024  exbiriVD  46025  rspsbc2VD  46026  tratrbVD  46032  ssralv2VD  46037  imbi12VD  46044  imbi13VD  46045  truniALTVD  46049  trintALTVD  46051  onfrALTlem2VD  46060