Theorem in3 38834

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 38808	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
3	2	dfvd2ir 38802	1 ⊢ (   𝜑   ,   𝜓   ▶   (𝜒 → 𝜃)   )

Syntax hints:   → wi 4  (   wvd2 38793  (   wvd3 38803

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 197  df-an 386  df-3an 1039  df-vd2 38794  df-vd3 38806

This theorem is referenced by:  e223  38860  suctrALT2VD  39071  en3lplem2VD  39079  exbirVD  39088  exbiriVD  39089  rspsbc2VD  39090  tratrbVD  39097  ssralv2VD  39102  imbi12VD  39109  imbi13VD  39110  truniALTVD  39114  trintALTVD  39116  onfrALTlem2VD  39125