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Mirrors > Home > ILE Home > Th. List > ishmeo | Unicode version |
Description: The predicate F is a homeomorphism between topology and topology . Proposition of [BourbakiTop1] p. I.2. (Contributed by FL, 14-Feb-2007.) (Revised by Mario Carneiro, 22-Aug-2015.) |
Ref | Expression |
---|---|
ishmeo |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-hmeo 12743 | . . 3 | |
2 | 1 | elmpocl 6019 | . 2 |
3 | df-cn 12630 | . . . 4 | |
4 | 3 | elmpocl 6019 | . . 3 |
5 | 4 | adantr 274 | . 2 |
6 | hmeofvalg 12745 | . . . 4 | |
7 | 6 | eleq2d 2227 | . . 3 |
8 | cnveq 4761 | . . . . 5 | |
9 | 8 | eleq1d 2226 | . . . 4 |
10 | 9 | elrab 2868 | . . 3 |
11 | 7, 10 | bitrdi 195 | . 2 |
12 | 2, 5, 11 | pm5.21nii 694 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wceq 1335 wcel 2128 wral 2435 crab 2439 cuni 3773 ccnv 4586 cima 4590 (class class class)co 5825 cmap 6594 ctop 12437 ccn 12627 chmeo 12742 |
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 4083 ax-pow 4136 ax-pr 4170 ax-un 4394 ax-setind 4497 |
This theorem depends on definitions: df-bi 116 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-ral 2440 df-rex 2441 df-rab 2444 df-v 2714 df-sbc 2938 df-csb 3032 df-dif 3104 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-uni 3774 df-iun 3852 df-br 3967 df-opab 4027 df-mpt 4028 df-id 4254 df-xp 4593 df-rel 4594 df-cnv 4595 df-co 4596 df-dm 4597 df-rn 4598 df-res 4599 df-ima 4600 df-iota 5136 df-fun 5173 df-fn 5174 df-f 5175 df-fv 5179 df-ov 5828 df-oprab 5829 df-mpo 5830 df-1st 6089 df-2nd 6090 df-map 6596 df-top 12438 df-topon 12451 df-cn 12630 df-hmeo 12743 |
This theorem is referenced by: hmeocn 12747 hmeocnvcn 12748 hmeocnv 12749 hmeores 12757 hmeoco 12758 idhmeo 12759 txhmeo 12761 txswaphmeo 12763 cnrehmeocntop 13035 |
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