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Theorem datisi 2053
 Description: "Datisi", one of the syllogisms of Aristotelian logic. All 𝜑 is 𝜓, and some 𝜑 is 𝜒, therefore some 𝜒 is 𝜓. (In Aristotelian notation, AII-3: MaP and MiS therefore SiP.) (Contributed by David A. Wheeler, 28-Aug-2016.)
Hypotheses
Ref Expression
datisi.maj 𝑥(𝜑𝜓)
datisi.min 𝑥(𝜑𝜒)
Assertion
Ref Expression
datisi 𝑥(𝜒𝜓)

Proof of Theorem datisi
StepHypRef Expression
1 datisi.min . 2 𝑥(𝜑𝜒)
2 simpr 108 . . 3 ((𝜑𝜒) → 𝜒)
3 datisi.maj . . . . 5 𝑥(𝜑𝜓)
43spi 1470 . . . 4 (𝜑𝜓)
54adantr 270 . . 3 ((𝜑𝜒) → 𝜓)
62, 5jca 300 . 2 ((𝜑𝜒) → (𝜒𝜓))
71, 6eximii 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:  ferison  2055
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