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Mirrors > Home > ILE Home > Th. List > supval2ti | Unicode version |
Description: Alternate expression for the supremum. (Contributed by Jim Kingdon, 23-Nov-2021.) |
Ref | Expression |
---|---|
supmoti.ti | |
supval2ti.ex |
Ref | Expression |
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supval2ti |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-sup 6879 | . 2 | |
2 | supmoti.ti | . . . 4 | |
3 | supval2ti.ex | . . . 4 | |
4 | 2, 3 | supeuti 6889 | . . 3 |
5 | riotauni 5744 | . . 3 | |
6 | 4, 5 | syl 14 | . 2 |
7 | 1, 6 | eqtr4id 2192 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wb 104 wceq 1332 wcel 1481 wral 2417 wrex 2418 wreu 2419 crab 2421 cuni 3744 class class class wbr 3937 crio 5737 csup 6877 |
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 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-fal 1338 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-rex 2423 df-reu 2424 df-rmo 2425 df-rab 2426 df-v 2691 df-sbc 2914 df-un 3080 df-sn 3538 df-pr 3539 df-op 3541 df-uni 3745 df-br 3938 df-iota 5096 df-riota 5738 df-sup 6879 |
This theorem is referenced by: eqsupti 6891 supclti 6893 supubti 6894 suplubti 6895 supelti 6897 infvalti 6917 |
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