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Mirrors > Home > MPE Home > Th. List > eltopss | Structured version Visualization version Unicode version |
Description: A member of a topology is a subset of its underlying set. (Contributed by NM, 12-Sep-2006.) |
Ref | Expression |
---|---|
1open.1 |
Ref | Expression |
---|---|
eltopss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elssuni 4467 | . . 3 | |
2 | 1open.1 | . . 3 | |
3 | 1, 2 | syl6sseqr 3652 | . 2 |
4 | 3 | adantl 482 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wceq 1483 wcel 1990 wss 3574 cuni 4436 ctop 20698 |
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-v 3202 df-in 3581 df-ss 3588 df-uni 4437 |
This theorem is referenced by: riinopn 20713 opncld 20837 ntrval2 20855 ntrss3 20864 cmclsopn 20866 opncldf1 20888 opnneissb 20918 opnssneib 20919 opnneiss 20922 neitr 20984 restntr 20986 cnpnei 21068 imasnopn 21493 cnextcn 21871 utopreg 22056 opnregcld 32325 ptrecube 33409 poimirlem29 33438 poimir 33442 |
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