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Theorem disamis 2088
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 1501 . . 3 (𝜑𝜒)
43anim1i 338 . 2 ((𝜑𝜓) → (𝜒𝜓))
51, 4eximii 1566 1 𝑥(𝜒𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  wal 1314  wex 1453
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1408  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-4 1472  ax-ial 1499
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  bocardo  2090
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