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Mirrors > Home > NFE Home > Th. List > elvvk | Unicode version |
Description: Membership in k (Contributed by SF, 13-Jan-2015.) |
Ref | Expression |
---|---|
elvvk | k |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elxpk 4196 | . 2 k | |
2 | vex 2862 | . . . . 5 | |
3 | vex 2862 | . . . . 5 | |
4 | 2, 3 | pm3.2i 441 | . . . 4 |
5 | 4 | biantru 491 | . . 3 |
6 | 5 | 2exbii 1583 | . 2 |
7 | 1, 6 | bitr4i 243 | 1 k |
Colors of variables: wff setvar class |
Syntax hints: wb 176 wa 358 wex 1541 wceq 1642 wcel 1710 cvv 2859 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-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: opkabssvvk 4208 ssrelk 4211 eqrelk 4212 insklem 4304 ltfinex 4464 setconslem4 4734 setconslem6 4736 |
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