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Mirrors > Home > ILE Home > Th. List > eltpsi | Unicode version |
Description: Properties that determine a topological space from a construction (using no explicit indices). (Contributed by NM, 20-Oct-2012.) (Revised by Mario Carneiro, 13-Aug-2015.) |
Ref | Expression |
---|---|
eltpsi.k | TopSet |
eltpsi.u | |
eltpsi.j |
Ref | Expression |
---|---|
eltpsi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eltpsi.j | . . 3 | |
2 | eltpsi.u | . . . 4 | |
3 | 2 | toptopon 12656 | . . 3 TopOn |
4 | 1, 3 | mpbi 144 | . 2 TopOn |
5 | eltpsi.k | . . 3 TopSet | |
6 | 5 | eltpsg 12678 | . 2 TopOn |
7 | 4, 6 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1343 wcel 2136 cpr 3577 cop 3579 cuni 3789 cfv 5188 cnx 12391 cbs 12394 TopSetcts 12463 ctop 12635 TopOnctopon 12648 ctps 12668 |
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 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-13 2138 ax-14 2139 ax-ext 2147 ax-coll 4097 ax-sep 4100 ax-pow 4153 ax-pr 4187 ax-un 4411 ax-setind 4514 ax-cnex 7844 ax-resscn 7845 ax-1cn 7846 ax-1re 7847 ax-icn 7848 ax-addcl 7849 ax-addrcl 7850 ax-mulcl 7851 ax-addcom 7853 ax-addass 7855 ax-i2m1 7858 ax-0lt1 7859 ax-0id 7861 ax-rnegex 7862 ax-pre-ltirr 7865 ax-pre-lttrn 7867 ax-pre-ltadd 7869 |
This theorem depends on definitions: df-bi 116 df-3an 970 df-tru 1346 df-fal 1349 df-nf 1449 df-sb 1751 df-eu 2017 df-mo 2018 df-clab 2152 df-cleq 2158 df-clel 2161 df-nfc 2297 df-ne 2337 df-nel 2432 df-ral 2449 df-rex 2450 df-reu 2451 df-rab 2453 df-v 2728 df-sbc 2952 df-csb 3046 df-dif 3118 df-un 3120 df-in 3122 df-ss 3129 df-nul 3410 df-pw 3561 df-sn 3582 df-pr 3583 df-op 3585 df-uni 3790 df-int 3825 df-iun 3868 df-br 3983 df-opab 4044 df-mpt 4045 df-id 4271 df-xp 4610 df-rel 4611 df-cnv 4612 df-co 4613 df-dm 4614 df-rn 4615 df-res 4616 df-ima 4617 df-iota 5153 df-fun 5190 df-fn 5191 df-f 5192 df-f1 5193 df-fo 5194 df-f1o 5195 df-fv 5196 df-ov 5845 df-oprab 5846 df-mpo 5847 df-1st 6108 df-2nd 6109 df-pnf 7935 df-mnf 7936 df-ltxr 7938 df-inn 8858 df-2 8916 df-3 8917 df-4 8918 df-5 8919 df-6 8920 df-7 8921 df-8 8922 df-9 8923 df-ndx 12397 df-slot 12398 df-base 12400 df-tset 12476 df-rest 12558 df-topn 12559 df-top 12636 df-topon 12649 df-topsp 12669 |
This theorem is referenced by: distps 12731 retps 13167 |
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