Theorem in3 44582

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 44565	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
3	2	dfvd2ir 44559	1 ⊢ (   𝜑   ,   𝜓   ▶   (𝜒 → 𝜃)   )

Syntax hints:   → wi 4  (   wvd2 44550  (   wvd3 44560

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 44551  df-vd3 44563

This theorem is referenced by:  e223  44608  suctrALT2VD  44808  en3lplem2VD  44816  exbirVD  44825  exbiriVD  44826  rspsbc2VD  44827  tratrbVD  44833  ssralv2VD  44838  imbi12VD  44845  imbi13VD  44846  truniALTVD  44850  trintALTVD  44852  onfrALTlem2VD  44861