Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > suplocexprlemss | Unicode version |
Description: Lemma for suplocexpr 7666. 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 2513 | . . . . . 6 | |
3 | ltrelpr 7446 | . . . . . . . 8 | |
4 | 3 | brel 4656 | . . . . . . 7 |
5 | 4 | simpld 111 | . . . . . 6 |
6 | 2, 5 | syl6 33 | . . . . 5 |
7 | 6 | a1i 9 | . . . 4 |
8 | 7 | rexlimdvw 2587 | . . 3 |
9 | 1, 8 | mpd 13 | . 2 |
10 | 9 | ssrdv 3148 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wo 698 wex 1480 wcel 2136 wral 2444 wrex 2445 wss 3116 class class class wbr 3982 cnp 7232 cltp 7236 |
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 1435 ax-7 1436 ax-gen 1437 ax-ie1 1481 ax-ie2 1482 ax-8 1492 ax-10 1493 ax-11 1494 ax-i12 1495 ax-bndl 1497 ax-4 1498 ax-17 1514 ax-i9 1518 ax-ial 1522 ax-i5r 1523 ax-14 2139 ax-ext 2147 ax-sep 4100 ax-pow 4153 ax-pr 4187 |
This theorem depends on definitions: df-bi 116 df-3an 970 df-tru 1346 df-nf 1449 df-sb 1751 df-clab 2152 df-cleq 2158 df-clel 2161 df-nfc 2297 df-ral 2449 df-rex 2450 df-v 2728 df-un 3120 df-in 3122 df-ss 3129 df-pw 3561 df-sn 3582 df-pr 3583 df-op 3585 df-br 3983 df-opab 4044 df-xp 4610 df-iltp 7411 |
This theorem is referenced by: suplocexprlemml 7657 suplocexprlemrl 7658 suplocexprlemmu 7659 suplocexprlemru 7660 suplocexprlemdisj 7661 suplocexprlemloc 7662 suplocexprlemex 7663 suplocexprlemub 7664 suplocexprlemlub 7665 |
Copyright terms: Public domain | W3C validator |