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Theorem in3 38660
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 38634 . 2 (𝜑 → (𝜓 → (𝜒𝜃)))
32dfvd2ir 38628 1 (   𝜑   ,   𝜓   ▶   (𝜒𝜃)   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd2 38619  (   wvd3 38629
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 197  df-an 386  df-3an 1039  df-vd2 38620  df-vd3 38632
This theorem is referenced by:  e223  38686  suctrALT2VD  38897  en3lplem2VD  38905  exbirVD  38914  exbiriVD  38915  rspsbc2VD  38916  tratrbVD  38923  ssralv2VD  38928  imbi12VD  38935  imbi13VD  38936  truniALTVD  38940  trintALTVD  38942  onfrALTlem2VD  38951
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