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Theorem datisi 2562
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 475 . . 3 ((𝜑𝜒) → 𝜒)
3 datisi.maj . . . . 5 𝑥(𝜑𝜓)
43spi 2041 . . . 4 (𝜑𝜓)
54adantr 479 . . 3 ((𝜑𝜒) → 𝜓)
62, 5jca 552 . 2 ((𝜑𝜒) → (𝜒𝜓))
71, 6eximii 1753 1 𝑥(𝜒𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382  wal 1472  wex 1694
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-12 2033
This theorem depends on definitions:  df-bi 195  df-an 384  df-ex 1695
This theorem is referenced by:  ferison  2564
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