Theorem in3 44592

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 44575	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
3	2	dfvd2ir 44569	1 ⊢ (   𝜑   ,   𝜓   ▶   (𝜒 → 𝜃)   )

Syntax hints:   → wi 4  (   wvd2 44560  (   wvd3 44570

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 207  df-an 396  df-3an 1088  df-vd2 44561  df-vd3 44573

This theorem is referenced by:  e223  44618  suctrALT2VD  44818  en3lplem2VD  44826  exbirVD  44835  exbiriVD  44836  rspsbc2VD  44837  tratrbVD  44843  ssralv2VD  44848  imbi12VD  44855  imbi13VD  44856  truniALTVD  44860  trintALTVD  44862  onfrALTlem2VD  44871