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| Mirrors > Home > ILE Home > Th. List > iccssre | Unicode version | ||
| Description: A closed real interval is a set of reals. (Contributed by FL, 6-Jun-2007.) (Proof shortened by Paul Chapman, 21-Jan-2008.) |
| Ref | Expression |
|---|---|
| iccssre |
|
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | elicc2 10095 |
. . . . 5
| |
| 2 | 1 | biimp3a 1358 |
. . . 4
|
| 3 | 2 | simp1d 1012 |
. . 3
|
| 4 | 3 | 3expia 1208 |
. 2
|
| 5 | 4 | ssrdv 3207 |
1
|
| 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 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-io 711 ax-5 1471 ax-7 1472 ax-gen 1473 ax-ie1 1517 ax-ie2 1518 ax-8 1528 ax-10 1529 ax-11 1530 ax-i12 1531 ax-bndl 1533 ax-4 1534 ax-17 1550 ax-i9 1554 ax-ial 1558 ax-i5r 1559 ax-13 2180 ax-14 2181 ax-ext 2189 ax-sep 4178 ax-pow 4234 ax-pr 4269 ax-un 4498 ax-setind 4603 ax-cnex 8051 ax-resscn 8052 ax-pre-ltirr 8072 ax-pre-ltwlin 8073 ax-pre-lttrn 8074 |
| This theorem depends on definitions: df-bi 117 df-3or 982 df-3an 983 df-tru 1376 df-fal 1379 df-nf 1485 df-sb 1787 df-eu 2058 df-mo 2059 df-clab 2194 df-cleq 2200 df-clel 2203 df-nfc 2339 df-ne 2379 df-nel 2474 df-ral 2491 df-rex 2492 df-rab 2495 df-v 2778 df-sbc 3006 df-dif 3176 df-un 3178 df-in 3180 df-ss 3187 df-pw 3628 df-sn 3649 df-pr 3650 df-op 3652 df-uni 3865 df-br 4060 df-opab 4122 df-id 4358 df-po 4361 df-iso 4362 df-xp 4699 df-rel 4700 df-cnv 4701 df-co 4702 df-dm 4703 df-iota 5251 df-fun 5292 df-fv 5298 df-ov 5970 df-oprab 5971 df-mpo 5972 df-pnf 8144 df-mnf 8145 df-xr 8146 df-ltxr 8147 df-le 8148 df-icc 10052 |
| This theorem is referenced by: iccsupr 10123 iccshftri 10152 iccshftli 10154 iccdili 10156 icccntri 10158 unitssre 10162 iccen 10163 cos12dec 12194 suplociccreex 15211 suplociccex 15212 dedekindicclemuub 15213 dedekindicclemlu 15217 dedekindicclemeu 15218 dedekindicclemicc 15219 dedekindicc 15220 reeff1olem 15358 cosz12 15367 ioocosf1o 15441 |
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