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Theorem camestres 2047
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.) (Revised by David A. Wheeler, 2-Sep-2016.)
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.min . . . 4 𝑥(𝜒 → ¬ 𝜓)
21spi 1470 . . 3 (𝜒 → ¬ 𝜓)
3 camestres.maj . . . 4 𝑥(𝜑𝜓)
43spi 1470 . . 3 (𝜑𝜓)
52, 4nsyl 591 . 2 (𝜒 → ¬ 𝜑)
65ax-gen 1379 1 𝑥(𝜒 → ¬ 𝜑)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wal 1283
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-in1 577  ax-in2 578  ax-gen 1379  ax-4 1441
This theorem is referenced by: (None)
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