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Theorem disamis 2054
 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 1470 . . 3 (𝜑𝜒)
43anim1i 333 . 2 ((𝜑𝜓) → (𝜒𝜓))
51, 4eximii 1534 1 𝑥(𝜒𝜓)
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 102  ∀wal 1283  ∃wex 1422 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-ial 1468 This theorem depends on definitions:  df-bi 115 This theorem is referenced by:  bocardo  2056
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