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Mirrors > Home > NFE Home > Th. List > opkelssetkg | Unicode version |
Description: Membership in the Kuratowski subset relationship. (Contributed by SF, 13-Jan-2015.) |
Ref | Expression |
---|---|
opkelssetkg | Sk |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ssetk 4193 | . 2 Sk | |
2 | sseq1 3292 | . 2 | |
3 | sseq2 3293 | . 2 | |
4 | 1, 2, 3 | opkelopkabg 4245 | 1 Sk |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wa 358 wcel 1710 wss 3257 copk 4057 Sk cssetk 4183 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 ax-nin 4078 ax-sn 4087 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-3an 936 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ne 2518 df-v 2861 df-nin 3211 df-compl 3212 df-in 3213 df-un 3214 df-dif 3215 df-ss 3259 df-nul 3551 df-sn 3741 df-pr 3742 df-opk 4058 df-ssetk 4193 |
This theorem is referenced by: elssetkg 4269 ssetkex 4294 dfidk2 4313 ssfin 4470 eqpwrelk 4478 srelk 4524 dfsset2 4743 |
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