Theorem in3 45346

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 45329	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
3	2	dfvd2ir 45323	1 ⊢ (   𝜑   ,   𝜓   ▶   (𝜒 → 𝜃)   )

This proof depends on syntax axioms:   → wi 4  (   wvd2 45314  (   wvd3 45324

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 401  df-3an 1105  df-vd2 45315  df-vd3 45327

This theorem is used by:  e223  45372  suctrALT2VD  45572  en3lplem2VD  45580  exbirVD  45589  exbiriVD  45590  rspsbc2VD  45591  tratrbVD  45597  ssralv2VD  45602  imbi12VD  45609  imbi13VD  45610  truniALTVD  45614  trintALTVD  45616  onfrALTlem2VD  45625