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Mirrors > Home > MPE Home > Th. List > restuni | Structured version Visualization version Unicode version |
Description: The underlying set of a subspace topology. (Contributed by FL, 5-Jan-2009.) (Revised by Mario Carneiro, 13-Aug-2015.) |
Ref | Expression |
---|---|
restuni.1 |
Ref | Expression |
---|---|
restuni | ↾t |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | restuni.1 | . . . 4 | |
2 | 1 | toptopon 20722 | . . 3 TopOn |
3 | resttopon 20965 | . . 3 TopOn ↾t TopOn | |
4 | 2, 3 | sylanb 489 | . 2 ↾t TopOn |
5 | toponuni 20719 | . 2 ↾t TopOn ↾t | |
6 | 4, 5 | syl 17 | 1 ↾t |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wceq 1483 wcel 1990 wss 3574 cuni 4436 cfv 5888 (class class class)co 6650 ↾t crest 16081 ctop 20698 TopOnctopon 20715 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-rep 4771 ax-sep 4781 ax-nul 4789 ax-pow 4843 ax-pr 4906 ax-un 6949 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3or 1038 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-rex 2918 df-reu 2919 df-rab 2921 df-v 3202 df-sbc 3436 df-csb 3534 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-pss 3590 df-nul 3916 df-if 4087 df-pw 4160 df-sn 4178 df-pr 4180 df-tp 4182 df-op 4184 df-uni 4437 df-int 4476 df-iun 4522 df-br 4654 df-opab 4713 df-mpt 4730 df-tr 4753 df-id 5024 df-eprel 5029 df-po 5035 df-so 5036 df-fr 5073 df-we 5075 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-pred 5680 df-ord 5726 df-on 5727 df-lim 5728 df-suc 5729 df-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-f1 5893 df-fo 5894 df-f1o 5895 df-fv 5896 df-ov 6653 df-oprab 6654 df-mpt2 6655 df-om 7066 df-1st 7168 df-2nd 7169 df-wrecs 7407 df-recs 7468 df-rdg 7506 df-oadd 7564 df-er 7742 df-en 7956 df-fin 7959 df-fi 8317 df-rest 16083 df-topgen 16104 df-top 20699 df-topon 20716 df-bases 20750 |
This theorem is referenced by: restuni2 20971 restcld 20976 restopn2 20981 neitr 20984 restcls 20985 restntr 20986 rncmp 21199 cmpsublem 21202 cmpsub 21203 fiuncmp 21207 connsubclo 21227 connima 21228 conncn 21229 nllyrest 21289 cldllycmp 21298 lly1stc 21299 llycmpkgen2 21353 1stckgen 21357 txkgen 21455 xkopjcn 21459 xkococnlem 21462 cnextfres1 21872 cnextfres 21873 cncfcnvcn 22724 cnheibor 22754 evthicc 23228 psercn 24180 abelth 24195 connpconn 31217 cvmscld 31255 cvmsss2 31256 cvmliftmolem1 31263 cvmliftlem10 31276 cvmlift2lem9 31293 cvmlift2lem11 31295 cvmlift2lem12 31296 cvmlift3lem7 31307 ivthALT 32330 ptrest 33408 poimirlem29 33438 poimirlem30 33439 poimirlem31 33440 poimir 33442 cncfuni 40099 cncfiooicclem1 40106 stoweidlem28 40245 dirkercncflem4 40323 fourierdlem42 40366 |
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