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Mirrors > Home > ILE Home > Th. List > supeuti | Unicode version |
Description: A supremum is unique. Similar to Theorem I.26 of [Apostol] p. 24 (but for suprema in general). (Contributed by Jim Kingdon, 23-Nov-2021.) |
Ref | Expression |
---|---|
supmoti.ti | |
supeuti.2 |
Ref | Expression |
---|---|
supeuti |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | supeuti.2 | . 2 | |
2 | supmoti.ti | . . 3 | |
3 | 2 | supmoti 6873 | . 2 |
4 | reu5 2641 | . 2 | |
5 | 1, 3, 4 | sylanbrc 413 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wb 104 wcel 1480 wral 2414 wrex 2415 wreu 2416 wrmo 2417 class class class wbr 3924 |
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-in1 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-fal 1337 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-reu 2421 df-rmo 2422 df-v 2683 df-un 3070 df-sn 3528 df-pr 3529 df-op 3531 df-br 3925 |
This theorem is referenced by: supval2ti 6875 eqsupti 6876 supclti 6878 supubti 6879 suplubti 6880 supelti 6882 |
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