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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 2106 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 1516 | . . . 4 |
4 | 3 | adantl 275 | . . 3 |
5 | simpl 108 | . . 3 | |
6 | 4, 5 | jca 304 | . 2 |
7 | 1, 6 | eximii 1582 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wal 1333 wex 1472 |
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 1427 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-4 1490 ax-ial 1514 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: (None) |
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