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Mirrors > Home > MPE Home > Th. List > haustop | Structured version Visualization version Unicode version |
Description: A Hausdorff space is a topology. (Contributed by NM, 5-Mar-2007.) |
Ref | Expression |
---|---|
haustop |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2622 | . . 3 | |
2 | 1 | ishaus 21126 | . 2 |
3 | 2 | simplbi 476 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 w3a 1037 wceq 1483 wcel 1990 wne 2794 wral 2912 wrex 2913 cin 3573 c0 3915 cuni 4436 ctop 20698 cha 21112 |
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-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-uni 4437 df-haus 21119 |
This theorem is referenced by: haust1 21156 resthaus 21172 sshaus 21179 lmmo 21184 hauscmplem 21209 hauscmp 21210 hauslly 21295 hausllycmp 21297 kgenhaus 21347 pthaus 21441 txhaus 21450 xkohaus 21456 haushmph 21595 cmphaushmeo 21603 hausflim 21785 hauspwpwf1 21791 hauspwpwdom 21792 hausflf 21801 cnextfun 21868 cnextfvval 21869 cnextf 21870 cnextcn 21871 cnextfres1 21872 cnextfres 21873 qtophaus 29903 ismntop 30070 poimirlem30 33439 hausgraph 37790 |
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