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Theorem camestres 2697
Description: "Camestres", one of the syllogisms of Aristotelian logic. All 𝜑 is 𝜓, and no 𝜒 is 𝜓, therefore no 𝜒 is 𝜑. In Aristotelian notation, AEE-2: PaM and SeM therefore SeP. (Contributed by David A. Wheeler, 28-Aug-2016.) Reduce dependencies on axioms. (Revised by BJ, 16-Sep-2022.)
Hypotheses
Ref Expression
camestres.maj 𝑥(𝜑𝜓)
camestres.min 𝑥(𝜒 → ¬ 𝜓)
Assertion
Ref Expression
camestres 𝑥(𝜒 → ¬ 𝜑)

Proof of Theorem camestres
StepHypRef Expression
1 camestres.maj . . 3 𝑥(𝜑𝜓)
2 con3 150 . . . 4 ((𝜑𝜓) → (¬ 𝜓 → ¬ 𝜑))
32alimi 1906 . . 3 (∀𝑥(𝜑𝜓) → ∀𝑥𝜓 → ¬ 𝜑))
41, 3ax-mp 5 . 2 𝑥𝜓 → ¬ 𝜑)
5 camestres.min . 2 𝑥(𝜒 → ¬ 𝜓)
64, 5celarent 2687 1 𝑥(𝜒 → ¬ 𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1650
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1890  ax-4 1904
This theorem depends on definitions:  df-bi 198  df-an 385
This theorem is referenced by:  camestros  2705  calemes  2716
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