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Mirrors > Home > ILE Home > Th. List > suprnubex | Unicode version |
Description: An upper bound is not less than the supremum of a nonempty bounded set of reals. (Contributed by Jim Kingdon, 19-Jan-2022.) |
Ref | Expression |
---|---|
suprubex.ex |
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suprubex.ss |
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suprlubex.b |
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Ref | Expression |
---|---|
suprnubex |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | suprubex.ex |
. . . 4
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2 | suprubex.ss |
. . . 4
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3 | suprlubex.b |
. . . 4
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4 | 1, 2, 3 | suprlubex 8802 |
. . 3
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5 | 4 | notbid 657 |
. 2
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6 | ralnex 2442 |
. 2
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7 | 5, 6 | bitr4di 197 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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 1481 ax-10 1482 ax-11 1483 ax-i12 1484 ax-bndl 1486 ax-4 1487 ax-17 1503 ax-i9 1507 ax-ial 1511 ax-i5r 1512 ax-13 2127 ax-14 2128 ax-ext 2136 ax-sep 4078 ax-pow 4130 ax-pr 4164 ax-un 4388 ax-setind 4490 ax-cnex 7802 ax-resscn 7803 ax-pre-ltirr 7823 ax-pre-ltwlin 7824 ax-pre-lttrn 7825 ax-pre-apti 7826 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-fal 1338 df-nf 1438 df-sb 1740 df-eu 2006 df-mo 2007 df-clab 2141 df-cleq 2147 df-clel 2150 df-nfc 2285 df-ne 2325 df-nel 2420 df-ral 2437 df-rex 2438 df-reu 2439 df-rmo 2440 df-rab 2441 df-v 2711 df-sbc 2934 df-dif 3100 df-un 3102 df-in 3104 df-ss 3111 df-pw 3541 df-sn 3562 df-pr 3563 df-op 3565 df-uni 3769 df-br 3962 df-opab 4022 df-po 4251 df-iso 4252 df-xp 4585 df-iota 5128 df-riota 5770 df-sup 6916 df-pnf 7893 df-mnf 7894 df-ltxr 7896 |
This theorem is referenced by: suprleubex 8804 |
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