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Mirrors > Home > MPE Home > Th. List > topbas | Structured version Visualization version Unicode version |
Description: A topology is its own basis. (Contributed by NM, 17-Jul-2006.) |
Ref | Expression |
---|---|
topbas |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | inopn 20704 | . . . . . . 7 | |
2 | 1 | 3expb 1266 | . . . . . 6 |
3 | simpr 477 | . . . . . . 7 | |
4 | ssid 3624 | . . . . . . 7 | |
5 | 3, 4 | jctir 561 | . . . . . 6 |
6 | eleq2 2690 | . . . . . . . 8 | |
7 | sseq1 3626 | . . . . . . . 8 | |
8 | 6, 7 | anbi12d 747 | . . . . . . 7 |
9 | 8 | rspcev 3309 | . . . . . 6 |
10 | 2, 5, 9 | syl2an2r 876 | . . . . 5 |
11 | 10 | exp31 630 | . . . 4 |
12 | 11 | ralrimdv 2968 | . . 3 |
13 | 12 | ralrimivv 2970 | . 2 |
14 | isbasis2g 20752 | . 2 | |
15 | 13, 14 | mpbird 247 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wceq 1483 wcel 1990 wral 2912 wrex 2913 cin 3573 wss 3574 ctop 20698 ctb 20749 |
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 ax-sep 4781 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 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-v 3202 df-in 3581 df-ss 3588 df-pw 4160 df-uni 4437 df-top 20699 df-bases 20750 |
This theorem is referenced by: resttop 20964 dis1stc 21302 txtop 21372 onpsstopbas 32429 |
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