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Theorem barbari 2382
 Description: "Barbari", one of the syllogisms of Aristotelian logic. All is , all is , and some exist, therefore some is . (In Aristotelian notation, AAI-1: MaP and SaM therefore SiP.) For example, given "All men are mortal", "All Greeks are men", and "Greeks exist", therefore "Some Greeks are mortal". Note the existence hypothesis (to prove the "some" in the conclusion). Example from https://en.wikipedia.org/wiki/Syllogism. (Contributed by David A. Wheeler, 27-Aug-2016.) (Revised by David A. Wheeler, 30-Aug-2016.)
Hypotheses
Ref Expression
barbari.maj
barbari.min
barbari.e
Assertion
Ref Expression
barbari

Proof of Theorem barbari
StepHypRef Expression
1 barbari.e . 2
2 barbari.maj . . . . 5
3 barbari.min . . . . 5
42, 3barbara 2378 . . . 4
54spi 1769 . . 3
65ancli 535 . 2
71, 6eximii 1587 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359  wal 1549  wex 1550 This theorem is referenced by:  celaront  2383 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-11 1761 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551
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