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Mirrors > Home > NFE Home > Th. List > cokrelk | Unicode version |
Description: A Kuratowski composition is a Kuratowski relationship. (Contributed by SF, 4-Feb-2015.) |
Ref | Expression |
---|---|
cokrelk | k k |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-cok 4190 | . . . . 5 k Ins2k Ins3k kk | |
2 | 1 | eleq2i 2417 | . . . 4 k Ins2k Ins3k kk |
3 | vex 2862 | . . . . 5 | |
4 | 3 | elimakv 4260 | . . . 4 Ins2k Ins3k kk Ins2k Ins3k k |
5 | 2, 4 | bitri 240 | . . 3 k Ins2k Ins3k k |
6 | inss1 3475 | . . . . . 6 Ins2k Ins3k k Ins2k | |
7 | 6 | sseli 3269 | . . . . 5 Ins2k Ins3k k Ins2k |
8 | vex 2862 | . . . . . . 7 | |
9 | opkelins2kg 4251 | . . . . . . 7 Ins2k | |
10 | 8, 3, 9 | mp2an 653 | . . . . . 6 Ins2k |
11 | vex 2862 | . . . . . . . . . . 11 | |
12 | vex 2862 | . . . . . . . . . . 11 | |
13 | 11, 12 | opkelxpk 4248 | . . . . . . . . . . 11 k |
14 | 11, 12, 13 | mpbir2an 886 | . . . . . . . . . 10 k |
15 | eleq1 2413 | . . . . . . . . . 10 k k | |
16 | 14, 15 | mpbiri 224 | . . . . . . . . 9 k |
17 | 16 | 3ad2ant2 977 | . . . . . . . 8 k |
18 | 17 | exlimiv 1634 | . . . . . . 7 k |
19 | 18 | exlimivv 1635 | . . . . . 6 k |
20 | 10, 19 | sylbi 187 | . . . . 5 Ins2k k |
21 | 7, 20 | syl 15 | . . . 4 Ins2k Ins3k k k |
22 | 21 | exlimiv 1634 | . . 3 Ins2k Ins3k k k |
23 | 5, 22 | sylbi 187 | . 2 k k |
24 | 23 | ssriv 3277 | 1 k k |
Colors of variables: wff setvar class |
Syntax hints: wb 176 w3a 934 wex 1541 wceq 1642 wcel 1710 cvv 2859 cin 3208 wss 3257 csn 3737 copk 4057 k cxpk 4174 kccnvk 4175 Ins2k cins2k 4176 Ins3k cins3k 4177 kcimak 4179 k ccomk 4180 |
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 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-rex 2620 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-xpk 4185 df-ins2k 4187 df-imak 4189 df-cok 4190 |
This theorem is referenced by: (None) |
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