Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > dimatis | Structured version Visualization version Unicode version |
Description: "Dimatis", one of the syllogisms of Aristotelian logic. Some is , and all is , therefore some is . (In Aristotelian notation, IAI-4: PiM and MaS therefore SiP.) For example, "Some pets are rabbits.", "All rabbits have fur", therefore "Some fur bearing animals are pets". Like darii 2565 with positions interchanged. (Contributed by David A. Wheeler, 28-Aug-2016.) |
Ref | Expression |
---|---|
dimatis.maj | |
dimatis.min |
Ref | Expression |
---|---|
dimatis |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dimatis.maj | . 2 | |
2 | dimatis.min | . . . . 5 | |
3 | 2 | spi 2054 | . . . 4 |
4 | 3 | adantl 482 | . . 3 |
5 | simpl 473 | . . 3 | |
6 | 4, 5 | jca 554 | . 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: (None) |
Copyright terms: Public domain | W3C validator |