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Theorem disamis 2725
Description: "Disamis", one of the syllogisms of Aristotelian logic. Some 𝜑 is 𝜓, and all 𝜑 is 𝜒, therefore some 𝜒 is 𝜓. (In Aristotelian notation, IAI-3: MiP and MaS therefore SiP.) (Contributed by David A. Wheeler, 28-Aug-2016.)
Hypotheses
Ref Expression
disamis.maj 𝑥(𝜑𝜓)
disamis.min 𝑥(𝜑𝜒)
Assertion
Ref Expression
disamis 𝑥(𝜒𝜓)

Proof of Theorem disamis
StepHypRef Expression
1 disamis.maj . 2 𝑥(𝜑𝜓)
2 disamis.min . . . 4 𝑥(𝜑𝜒)
32spi 2208 . . 3 (𝜑𝜒)
43anim1i 602 . 2 ((𝜑𝜓) → (𝜒𝜓))
51, 4eximii 1912 1 𝑥(𝜒𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382  wal 1629  wex 1852
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-12 2203
This theorem depends on definitions:  df-bi 197  df-an 383  df-ex 1853
This theorem is referenced by:  bocardo  2727
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