Theorem in3 42229

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 42212	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
3	2	dfvd2ir 42206	1 ⊢ (   𝜑   ,   𝜓   ▶   (𝜒 → 𝜃)   )

Syntax hints:   → wi 4  (   wvd2 42197  (   wvd3 42207

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 206  df-an 397  df-3an 1088  df-vd2 42198  df-vd3 42210

This theorem is referenced by:  e223  42255  suctrALT2VD  42456  en3lplem2VD  42464  exbirVD  42473  exbiriVD  42474  rspsbc2VD  42475  tratrbVD  42481  ssralv2VD  42486  imbi12VD  42493  imbi13VD  42494  truniALTVD  42498  trintALTVD  42500  onfrALTlem2VD  42509