Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > 0opn | Unicode version |
Description: The empty set is an open subset of any topology. (Contributed by Stefan Allan, 27-Feb-2006.) |
Ref | Expression |
---|---|
0opn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | uni0 3763 | . 2 | |
2 | 0ss 3401 | . . 3 | |
3 | uniopn 12173 | . . 3 | |
4 | 2, 3 | mpan2 421 | . 2 |
5 | 1, 4 | eqeltrrid 2227 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1480 wss 3071 c0 3363 cuni 3736 ctop 12169 |
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 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-fal 1337 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-dif 3073 df-in 3077 df-ss 3084 df-nul 3364 df-pw 3512 df-sn 3533 df-uni 3737 df-top 12170 |
This theorem is referenced by: 0ntop 12179 topgele 12201 istps 12204 topontopn 12209 tgclb 12239 en1top 12251 topcld 12283 ntr0 12308 0nei 12340 restrcl 12341 rest0 12353 mopn0 12662 |
Copyright terms: Public domain | W3C validator |