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Mirrors > Home > ILE Home > Th. List > celaront | Unicode version |
Description: "Celaront", one of the syllogisms of Aristotelian logic. No is , all is , and some exist, therefore some is not . (In Aristotelian notation, EAO-1: MeP and SaM therefore SoP.) For example, given "No reptiles have fur", "All snakes are reptiles.", and "Snakes exist.", prove "Some snakes have no fur". Note the existence hypothesis. Example from https://en.wikipedia.org/wiki/Syllogism. (Contributed by David A. Wheeler, 27-Aug-2016.) (Revised by David A. Wheeler, 2-Sep-2016.) |
Ref | Expression |
---|---|
celaront.maj | |
celaront.min | |
celaront.e |
Ref | Expression |
---|---|
celaront |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | celaront.maj | . 2 | |
2 | celaront.min | . 2 | |
3 | celaront.e | . 2 | |
4 | 1, 2, 3 | barbari 2079 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wal 1314 wex 1453 |
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 1408 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-4 1472 ax-ial 1499 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: (None) |
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