Theorem in3 45396

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 45379	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
3	2	dfvd2ir 45373	1 ⊢ (   𝜑   ,   𝜓   ▶   (𝜒 → 𝜃)   )

This proof depends on syntax axioms:   → wi 4  (   wvd2 45364  (   wvd3 45374

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 45365  df-vd3 45377

This theorem is used by:  e223  45422  suctrALT2VD  45622  en3lplem2VD  45630  exbirVD  45639  exbiriVD  45640  rspsbc2VD  45641  tratrbVD  45647  ssralv2VD  45652  imbi12VD  45659  imbi13VD  45660  truniALTVD  45664  trintALTVD  45666  onfrALTlem2VD  45675