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Theorem pm3.2an3 1232
Description: Version of pm3.2 461 for a triple conjunction. (Contributed by Alan Sare, 24-Oct-2011.) (Proof shortened by Kyle Wyonch, 24-Apr-2021.)
Assertion
Ref Expression
pm3.2an3 (𝜑 → (𝜓 → (𝜒 → (𝜑𝜓𝜒))))

Proof of Theorem pm3.2an3
StepHypRef Expression
1 df-3an 1032 . . 3 ((𝜑𝜓𝜒) ↔ ((𝜑𝜓) ∧ 𝜒))
21biimpri 216 . 2 (((𝜑𝜓) ∧ 𝜒) → (𝜑𝜓𝜒))
32exp31 627 1 (𝜑 → (𝜓 → (𝜒 → (𝜑𝜓𝜒))))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382  w3a 1030
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 195  df-an 384  df-3an 1032
This theorem is referenced by:  3exp  1255  tratrb  37550  19.21a3con13vVD  37892  tratrbVD  37902
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