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Theorem in3 39353
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 39327 . 2 (𝜑 → (𝜓 → (𝜒𝜃)))
32dfvd2ir 39321 1 (   𝜑   ,   𝜓   ▶   (𝜒𝜃)   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd2 39312  (   wvd3 39322
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 383  df-3an 1072  df-vd2 39313  df-vd3 39325
This theorem is referenced by:  e223  39379  suctrALT2VD  39587  en3lplem2VD  39595  exbirVD  39604  exbiriVD  39605  rspsbc2VD  39606  tratrbVD  39613  ssralv2VD  39618  imbi12VD  39625  imbi13VD  39626  truniALTVD  39630  trintALTVD  39632  onfrALTlem2VD  39641
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