Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > topgrptsetd | Unicode version |
Description: The topology of a constructed topological group. (Contributed by Mario Carneiro, 29-Aug-2015.) (Revised by Jim Kingdon, 9-Feb-2023.) |
Ref | Expression |
---|---|
topgrpfn.w | TopSet |
topgrpfnd.b | |
topgrpfnd.p | |
topgrpfnd.j |
Ref | Expression |
---|---|
topgrptsetd | TopSet |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tsetslid 12340 | . 2 TopSet Slot TopSet TopSet | |
2 | topgrpfn.w | . . 3 TopSet | |
3 | topgrpfnd.b | . . 3 | |
4 | topgrpfnd.p | . . 3 | |
5 | topgrpfnd.j | . . 3 | |
6 | 2, 3, 4, 5 | topgrpstrd 12341 | . 2 Struct |
7 | 1 | simpri 112 | . . . . 5 TopSet |
8 | opexg 4188 | . . . . 5 TopSet TopSet | |
9 | 7, 5, 8 | sylancr 411 | . . . 4 TopSet |
10 | tpid3g 3674 | . . . 4 TopSet TopSet TopSet | |
11 | 9, 10 | syl 14 | . . 3 TopSet TopSet |
12 | 11, 2 | eleqtrrdi 2251 | . 2 TopSet |
13 | 1, 6, 5, 12 | opelstrsl 12286 | 1 TopSet |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1335 wcel 2128 cvv 2712 ctp 3562 cop 3563 cfv 5170 c1 7733 cn 8833 c9 8891 cnx 12187 Slot cslot 12189 cbs 12190 cplusg 12252 TopSetcts 12258 |
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-in1 604 ax-in2 605 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-13 2130 ax-14 2131 ax-ext 2139 ax-sep 4082 ax-pow 4135 ax-pr 4169 ax-un 4393 ax-setind 4496 ax-cnex 7823 ax-resscn 7824 ax-1cn 7825 ax-1re 7826 ax-icn 7827 ax-addcl 7828 ax-addrcl 7829 ax-mulcl 7830 ax-addcom 7832 ax-addass 7834 ax-distr 7836 ax-i2m1 7837 ax-0lt1 7838 ax-0id 7840 ax-rnegex 7841 ax-cnre 7843 ax-pre-ltirr 7844 ax-pre-ltwlin 7845 ax-pre-lttrn 7846 ax-pre-apti 7847 ax-pre-ltadd 7848 |
This theorem depends on definitions: df-bi 116 df-3or 964 df-3an 965 df-tru 1338 df-fal 1341 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ne 2328 df-nel 2423 df-ral 2440 df-rex 2441 df-reu 2442 df-rab 2444 df-v 2714 df-sbc 2938 df-dif 3104 df-un 3106 df-in 3108 df-ss 3115 df-nul 3395 df-pw 3545 df-sn 3566 df-pr 3567 df-tp 3568 df-op 3569 df-uni 3773 df-int 3808 df-br 3966 df-opab 4026 df-mpt 4027 df-id 4253 df-xp 4592 df-rel 4593 df-cnv 4594 df-co 4595 df-dm 4596 df-rn 4597 df-res 4598 df-ima 4599 df-iota 5135 df-fun 5172 df-fn 5173 df-f 5174 df-fv 5178 df-riota 5780 df-ov 5827 df-oprab 5828 df-mpo 5829 df-pnf 7914 df-mnf 7915 df-xr 7916 df-ltxr 7917 df-le 7918 df-sub 8048 df-neg 8049 df-inn 8834 df-2 8892 df-3 8893 df-4 8894 df-5 8895 df-6 8896 df-7 8897 df-8 8898 df-9 8899 df-n0 9091 df-z 9168 df-uz 9440 df-fz 9913 df-struct 12192 df-ndx 12193 df-slot 12194 df-base 12196 df-plusg 12265 df-tset 12271 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |