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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 6848 | . 2 |
4 | reu5 2620 | . 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 1465 wral 2393 wrex 2394 wreu 2395 wrmo 2396 class class class wbr 3899 |
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 588 ax-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-fal 1322 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-reu 2400 df-rmo 2401 df-v 2662 df-un 3045 df-sn 3503 df-pr 3504 df-op 3506 df-br 3900 |
This theorem is referenced by: supval2ti 6850 eqsupti 6851 supclti 6853 supubti 6854 suplubti 6855 supelti 6857 |
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