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Theorem datisi 2087
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 109 . . 3 ((𝜑𝜒) → 𝜒)
3 datisi.maj . . . . 5 𝑥(𝜑𝜓)
43spi 1501 . . . 4 (𝜑𝜓)
54adantr 274 . . 3 ((𝜑𝜒) → 𝜓)
62, 5jca 304 . 2 ((𝜑𝜒) → (𝜒𝜓))
71, 6eximii 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:  ferison  2089
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