Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > bndndx | Unicode version |
Description: A bounded real sequence is less than or equal to at least one of its indices. (Contributed by NM, 18-Jan-2008.) |
Ref | Expression |
---|---|
bndndx |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | arch 8285 | . . . 4 | |
2 | nnre 8046 | . . . . . 6 | |
3 | lelttr 7199 | . . . . . . . . . . 11 | |
4 | ltle 7198 | . . . . . . . . . . . 12 | |
5 | 4 | 3adant2 957 | . . . . . . . . . . 11 |
6 | 3, 5 | syld 44 | . . . . . . . . . 10 |
7 | 6 | exp5o 1157 | . . . . . . . . 9 |
8 | 7 | com3l 80 | . . . . . . . 8 |
9 | 8 | imp4b 342 | . . . . . . 7 |
10 | 9 | com23 77 | . . . . . 6 |
11 | 2, 10 | sylan2 280 | . . . . 5 |
12 | 11 | reximdva 2463 | . . . 4 |
13 | 1, 12 | mpd 13 | . . 3 |
14 | r19.35-1 2504 | . . 3 | |
15 | 13, 14 | syl 14 | . 2 |
16 | 15 | rexlimiv 2471 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 w3a 919 wcel 1433 wral 2348 wrex 2349 class class class wbr 3785 cr 6980 clt 7153 cle 7154 cn 8039 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 576 ax-in2 577 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-13 1444 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pow 3948 ax-pr 3964 ax-un 4188 ax-setind 4280 ax-cnex 7067 ax-resscn 7068 ax-1re 7070 ax-addrcl 7073 ax-pre-ltirr 7088 ax-pre-ltwlin 7089 ax-pre-lttrn 7090 ax-arch 7095 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-fal 1290 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ne 2246 df-nel 2340 df-ral 2353 df-rex 2354 df-rab 2357 df-v 2603 df-dif 2975 df-un 2977 df-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-uni 3602 df-int 3637 df-br 3786 df-opab 3840 df-xp 4369 df-cnv 4371 df-pnf 7155 df-mnf 7156 df-xr 7157 df-ltxr 7158 df-le 7159 df-inn 8040 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |