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Mirrors > Home > ILE Home > Th. List > dimatis | 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 2119 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 1529 | . . . 4 |
4 | 3 | adantl 275 | . . 3 |
5 | simpl 108 | . . 3 | |
6 | 4, 5 | jca 304 | . 2 |
7 | 1, 6 | eximii 1595 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wal 1346 wex 1485 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1440 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-4 1503 ax-ial 1527 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: (None) |
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