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Theorem in3 41935
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 41918 . 2 (𝜑 → (𝜓 → (𝜒𝜃)))
32dfvd2ir 41912 1 (   𝜑   ,   𝜓   ▶   (𝜒𝜃)   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd2 41903  (   wvd3 41913
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 1091  df-vd2 41904  df-vd3 41916
This theorem is referenced by:  e223  41961  suctrALT2VD  42162  en3lplem2VD  42170  exbirVD  42179  exbiriVD  42180  rspsbc2VD  42181  tratrbVD  42187  ssralv2VD  42192  imbi12VD  42199  imbi13VD  42200  truniALTVD  42204  trintALTVD  42206  onfrALTlem2VD  42215
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