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Mirrors > Home > ILE Home > Th. List > calemos | Unicode version |
Description: "Calemos", one of the syllogisms of Aristotelian logic. All is (PaM), no is (MeS), and exist, therefore some is not (SoP). (In Aristotelian notation, AEO-4: PaM and MeS therefore SoP.) (Contributed by David A. Wheeler, 28-Aug-2016.) (Revised by David A. Wheeler, 2-Sep-2016.) |
Ref | Expression |
---|---|
calemos.maj | |
calemos.min | |
calemos.e |
Ref | Expression |
---|---|
calemos |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | calemos.e | . 2 | |
2 | calemos.min | . . . . . 6 | |
3 | 2 | spi 1429 | . . . . 5 |
4 | 3 | con2i 557 | . . . 4 |
5 | calemos.maj | . . . . 5 | |
6 | 5 | spi 1429 | . . . 4 |
7 | 4, 6 | nsyl 558 | . . 3 |
8 | 7 | ancli 306 | . 2 |
9 | 1, 8 | eximii 1493 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 97 wal 1241 wex 1381 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-5 1336 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-4 1400 ax-ial 1427 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: (None) |
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