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Mirrors > Home > ILE Home > Th. List > supclti | Unicode version |
Description: A supremum belongs to its base class (closure law). See also supubti 6879 and suplubti 6880. (Contributed by Jim Kingdon, 24-Nov-2021.) |
Ref | Expression |
---|---|
supmoti.ti | |
supclti.2 |
Ref | Expression |
---|---|
supclti |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | supmoti.ti | . . 3 | |
2 | supclti.2 | . . 3 | |
3 | 1, 2 | supval2ti 6875 | . 2 |
4 | 1, 2 | supeuti 6874 | . . 3 |
5 | riotacl 5737 | . . 3 | |
6 | 4, 5 | syl 14 | . 2 |
7 | 3, 6 | eqeltrd 2214 | 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 class class class wbr 3924 crio 5722 csup 6862 |
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-rab 2423 df-v 2683 df-sbc 2905 df-un 3070 df-in 3072 df-ss 3079 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-br 3925 df-iota 5083 df-riota 5723 df-sup 6864 |
This theorem is referenced by: suplub2ti 6881 supelti 6882 supisoti 6890 infclti 6903 inflbti 6904 infglbti 6905 suprubex 8702 suprleubex 8705 sup3exmid 8708 suprzclex 9142 supminfex 9385 maxleast 10978 zsupcl 11629 dvdslegcd 11642 |
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