Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > barbari | Structured version Visualization version 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 2563 | . . . 4 |
5 | 4 | spi 2054 | . . 3 |
6 | 5 | ancli 574 | . 2 |
7 | 1, 6 | eximii 1764 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wal 1481 wex 1704 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-12 2047 |
This theorem depends on definitions: df-bi 197 df-an 386 df-ex 1705 |
This theorem is referenced by: celaront 2568 |
Copyright terms: Public domain | W3C validator |