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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 6949 | . 2 |
4 | reu5 2676 | . 2 | |
5 | 1, 3, 4 | sylanbrc 414 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wb 104 wcel 2135 wral 2442 wrex 2443 wreu 2444 wrmo 2445 class class class wbr 3976 |
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 604 ax-in2 605 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-fal 1348 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-reu 2449 df-rmo 2450 df-v 2723 df-un 3115 df-sn 3576 df-pr 3577 df-op 3579 df-br 3977 |
This theorem is referenced by: supval2ti 6951 eqsupti 6952 supclti 6954 supubti 6955 suplubti 6956 supelti 6958 |
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