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Theorem in3 44020
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   ▶   (𝜒𝜃)   )

Proof of Theorem in3
StepHypRef Expression
1 in3.1 . . 3 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )
21dfvd3i 44003 . 2 (𝜑 → (𝜓 → (𝜒𝜃)))
32dfvd2ir 43997 1 (   𝜑   ,   𝜓   ▶   (𝜒𝜃)   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd2 43988  (   wvd3 43998
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 396  df-3an 1087  df-vd2 43989  df-vd3 44001
This theorem is referenced by:  e223  44046  suctrALT2VD  44247  en3lplem2VD  44255  exbirVD  44264  exbiriVD  44265  rspsbc2VD  44266  tratrbVD  44272  ssralv2VD  44277  imbi12VD  44284  imbi13VD  44285  truniALTVD  44289  trintALTVD  44291  onfrALTlem2VD  44300
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