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Mirrors > Home > ILE Home > Th. List > suplocexprlemss | Unicode version |
Description: Lemma for suplocexpr 7645. is a set of positive reals. (Contributed by Jim Kingdon, 7-Jan-2024.) |
Ref | Expression |
---|---|
suplocexpr.m | |
suplocexpr.ub | |
suplocexpr.loc |
Ref | Expression |
---|---|
suplocexprlemss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | suplocexpr.ub | . . 3 | |
2 | rsp 2504 | . . . . . 6 | |
3 | ltrelpr 7425 | . . . . . . . 8 | |
4 | 3 | brel 4638 | . . . . . . 7 |
5 | 4 | simpld 111 | . . . . . 6 |
6 | 2, 5 | syl6 33 | . . . . 5 |
7 | 6 | a1i 9 | . . . 4 |
8 | 7 | rexlimdvw 2578 | . . 3 |
9 | 1, 8 | mpd 13 | . 2 |
10 | 9 | ssrdv 3134 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wo 698 wex 1472 wcel 2128 wral 2435 wrex 2436 wss 3102 class class class wbr 3965 cnp 7211 cltp 7215 |
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-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4082 ax-pow 4135 ax-pr 4169 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-br 3966 df-opab 4026 df-xp 4592 df-iltp 7390 |
This theorem is referenced by: suplocexprlemml 7636 suplocexprlemrl 7637 suplocexprlemmu 7638 suplocexprlemru 7639 suplocexprlemdisj 7640 suplocexprlemloc 7641 suplocexprlemex 7642 suplocexprlemub 7643 suplocexprlemlub 7644 |
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