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Mirrors > Home > NFE Home > Th. List > opkelidkg | Unicode version |
Description: Membership in the Kuratowski identity relationship. (Contributed by SF, 13-Jan-2015.) |
Ref | Expression |
---|---|
opkelidkg | k |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-idk 4196 | . 2 k | |
2 | eqeq1 2359 | . 2 | |
3 | eqeq2 2362 | . 2 | |
4 | 1, 2, 3 | opkelopkabg 4246 | 1 k |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wa 358 wceq 1642 wcel 1710 copk 4058 k cidk 4185 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 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 4079 ax-sn 4088 |
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 2479 df-ne 2519 df-v 2862 df-nin 3212 df-compl 3213 df-in 3214 df-un 3215 df-dif 3216 df-ss 3260 df-nul 3552 df-sn 3742 df-pr 3743 df-opk 4059 df-idk 4196 |
This theorem is referenced by: dfidk2 4314 nnsucelrlem1 4425 nndisjeq 4430 eqtfinrelk 4487 oddfinex 4505 evenodddisjlem1 4516 dfphi2 4570 |
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