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Mirrors > Home > NFE Home > Th. List > eqrelk | Unicode version |
Description: Equality for two Kuratowski relationships. (Contributed by SF, 13-Jan-2015.) |
Ref | Expression |
---|---|
eqrelk | k k |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssofeq 4077 | . 2 k k k | |
2 | df-ral 2619 | . . 3 k k | |
3 | elvvk 4207 | . . . . . . 7 k | |
4 | 3 | imbi1i 315 | . . . . . 6 k |
5 | 19.23vv 1892 | . . . . . 6 | |
6 | 4, 5 | bitr4i 243 | . . . . 5 k |
7 | 6 | albii 1566 | . . . 4 k |
8 | alrot3 1738 | . . . 4 | |
9 | 7, 8 | bitri 240 | . . 3 k |
10 | opkex 4113 | . . . . 5 | |
11 | eleq1 2413 | . . . . . 6 | |
12 | eleq1 2413 | . . . . . 6 | |
13 | 11, 12 | bibi12d 312 | . . . . 5 |
14 | 10, 13 | ceqsalv 2885 | . . . 4 |
15 | 14 | 2albii 1567 | . . 3 |
16 | 2, 9, 15 | 3bitri 262 | . 2 k |
17 | 1, 16 | syl6bb 252 | 1 k k |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wa 358 wal 1540 wex 1541 wceq 1642 wcel 1710 wral 2614 cvv 2859 wss 3257 copk 4057 k cxpk 4174 |
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-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-ral 2619 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 |
This theorem is referenced by: eqrelkriiv 4213 eqrelkrdv 4214 cnvkexg 4286 ssetkex 4294 |
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