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Mirrors > Home > MPE Home > Th. List > hmeoqtop | Structured version Visualization version Unicode version |
Description: A homeomorphism is a quotient map. (Contributed by Mario Carneiro, 25-Aug-2015.) |
Ref | Expression |
---|---|
hmeoqtop |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hmeocn 20852 |
. . . 4
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2 | cntop2 20334 |
. . . 4
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3 | 1, 2 | syl 17 |
. . 3
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4 | eqid 2471 |
. . . 4
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5 | 4 | toptopon 20025 |
. . 3
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6 | 3, 5 | sylib 201 |
. 2
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7 | eqid 2471 |
. . . 4
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8 | 7, 4 | hmeof1o 20856 |
. . 3
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9 | f1ofo 5835 |
. . 3
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10 | forn 5809 |
. . 3
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11 | 8, 9, 10 | 3syl 18 |
. 2
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12 | hmeoima 20857 |
. 2
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13 | 6, 1, 11, 12 | qtopomap 20810 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1677 ax-4 1690 ax-5 1766 ax-6 1813 ax-7 1859 ax-8 1906 ax-9 1913 ax-10 1932 ax-11 1937 ax-12 1950 ax-13 2104 ax-ext 2451 ax-rep 4508 ax-sep 4518 ax-nul 4527 ax-pow 4579 ax-pr 4639 ax-un 6602 |
This theorem depends on definitions: df-bi 190 df-or 377 df-an 378 df-3an 1009 df-tru 1455 df-ex 1672 df-nf 1676 df-sb 1806 df-eu 2323 df-mo 2324 df-clab 2458 df-cleq 2464 df-clel 2467 df-nfc 2601 df-ne 2643 df-ral 2761 df-rex 2762 df-reu 2763 df-rab 2765 df-v 3033 df-sbc 3256 df-csb 3350 df-dif 3393 df-un 3395 df-in 3397 df-ss 3404 df-nul 3723 df-if 3873 df-pw 3944 df-sn 3960 df-pr 3962 df-op 3966 df-uni 4191 df-iun 4271 df-br 4396 df-opab 4455 df-mpt 4456 df-id 4754 df-xp 4845 df-rel 4846 df-cnv 4847 df-co 4848 df-dm 4849 df-rn 4850 df-res 4851 df-ima 4852 df-iota 5553 df-fun 5591 df-fn 5592 df-f 5593 df-f1 5594 df-fo 5595 df-f1o 5596 df-fv 5597 df-ov 6311 df-oprab 6312 df-mpt2 6313 df-map 7492 df-qtop 15484 df-top 19998 df-topon 20000 df-cn 20320 df-hmeo 20847 |
This theorem is referenced by: xpstopnlem2 20903 |
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