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Mirrors > Home > NFE Home > Th. List > opkelins2kg | Unicode version |
Description: Kuratowski ordered pair membership in Kuratowski insertion operator. (Contributed by SF, 12-Jan-2015.) |
Ref | Expression |
---|---|
opkelins2kg | Ins2k |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ins2k 4187 | . 2 Ins2k | |
2 | eqeq1 2359 | . . . 4 | |
3 | 2 | 3anbi1d 1256 | . . 3 |
4 | 3 | 3exbidv 1629 | . 2 |
5 | eqeq1 2359 | . . . 4 | |
6 | 5 | 3anbi2d 1257 | . . 3 |
7 | 6 | 3exbidv 1629 | . 2 |
8 | 1, 4, 7 | opkelopkabg 4245 | 1 Ins2k |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wa 358 w3a 934 wex 1541 wceq 1642 wcel 1710 csn 3737 copk 4057 Ins2k cins2k 4176 |
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-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-ins2k 4187 |
This theorem is referenced by: otkelins2kg 4253 opkelcokg 4261 ins2kss 4279 cokrelk 4284 |
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