Theorem in3 41315

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 41298	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
3	2	dfvd2ir 41292	1 ⊢ (   𝜑   ,   𝜓   ▶   (𝜒 → 𝜃)   )

Syntax hints:   → wi 4  (   wvd2 41283  (   wvd3 41293

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 210  df-an 400  df-3an 1086  df-vd2 41284  df-vd3 41296

This theorem is referenced by:  e223  41341  suctrALT2VD  41542  en3lplem2VD  41550  exbirVD  41559  exbiriVD  41560  rspsbc2VD  41561  tratrbVD  41567  ssralv2VD  41572  imbi12VD  41579  imbi13VD  41580  truniALTVD  41584  trintALTVD  41586  onfrALTlem2VD  41595