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Theorem in3 40949
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 40932 . 2 (𝜑 → (𝜓 → (𝜒𝜃)))
32dfvd2ir 40926 1 (   𝜑   ,   𝜓   ▶   (𝜒𝜃)   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd2 40917  (   wvd3 40927
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 209  df-an 399  df-3an 1085  df-vd2 40918  df-vd3 40930
This theorem is referenced by:  e223  40975  suctrALT2VD  41176  en3lplem2VD  41184  exbirVD  41193  exbiriVD  41194  rspsbc2VD  41195  tratrbVD  41201  ssralv2VD  41206  imbi12VD  41213  imbi13VD  41214  truniALTVD  41218  trintALTVD  41220  onfrALTlem2VD  41229
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