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Mirrors > Home > ILE Home > Th. List > barbari | Unicode version |
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.) |
Ref | Expression |
---|---|
barbari.maj | |
barbari.min | |
barbari.e |
Ref | Expression |
---|---|
barbari |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | barbari.e | . 2 | |
2 | barbari.maj | . . . . 5 | |
3 | barbari.min | . . . . 5 | |
4 | 2, 3 | barbara 2039 | . . . 4 |
5 | 4 | spi 1469 | . . 3 |
6 | 5 | ancli 316 | . 2 |
7 | 1, 6 | eximii 1533 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wal 1282 wex 1421 |
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 1376 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-4 1440 ax-ial 1467 |
This theorem depends on definitions: df-bi 115 |
This theorem is referenced by: celaront 2044 |
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