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Mirrors > Home > NFE Home > Th. List > opkelcnvk | Unicode version |
Description: Kuratowski ordered pair membership in a Kuratowski converse. (Contributed by SF, 14-Jan-2015.) |
Ref | Expression |
---|---|
opkelcnvk.1 | |
opkelcnvk.2 |
Ref | Expression |
---|---|
opkelcnvk | k |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opkelcnvk.1 | . 2 | |
2 | opkelcnvk.2 | . 2 | |
3 | opkelcnvkg 4249 | . 2 k | |
4 | 1, 2, 3 | mp2an 653 | 1 k |
Colors of variables: wff setvar class |
Syntax hints: wb 176 wcel 1710 cvv 2859 copk 4057 kccnvk 4175 |
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-cnvk 4186 |
This theorem is referenced by: opkelimagekg 4271 cnvkxpk 4276 cnvkexg 4286 dfidk2 4313 dfuni3 4315 dfint3 4318 nncaddccl 4419 nnsucelrlem1 4424 preaddccan2lem1 4454 ltfintrilem1 4465 ncfinlowerlem1 4482 eqtfinrelk 4486 oddfinex 4504 evenodddisjlem1 4515 nnpweqlem1 4522 sfintfinlem1 4531 tfinnnlem1 4533 vfinspclt 4552 dfop2lem1 4573 dfproj12 4576 dfproj22 4577 phialllem1 4616 setconslem1 4731 setconslem2 4732 setconslem4 4734 |
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