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Theorem barbari 2244
 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 . . . . . 6
3 barbari.min . . . . . 6
42, 3barbara 2240 . . . . 5
54spi 1738 . . . 4
65ancli 534 . . 3
76eximi 1563 . 2
81, 7ax-mp 8 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 358  wal 1527  wex 1528 This theorem is referenced by:  celaront  2245 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-11 1715 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529
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