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Mirrors > Home > NFE Home > Th. List > idkex | GIF version |
Description: The Kuratowski identity relationship is a set. (Contributed by SF, 14-Jan-2015.) |
Ref | Expression |
---|---|
idkex | ⊢ Ik ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfidk2 4313 | . 2 ⊢ Ik = ( Sk ∩ ◡k Sk ) | |
2 | ssetkex 4294 | . . 3 ⊢ Sk ∈ V | |
3 | 2 | cnvkex 4287 | . . 3 ⊢ ◡k Sk ∈ V |
4 | 2, 3 | inex 4105 | . 2 ⊢ ( Sk ∩ ◡k Sk ) ∈ V |
5 | 1, 4 | eqeltri 2423 | 1 ⊢ Ik ∈ V |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 1710 Vcvv 2859 ∩ cin 3208 ◡kccnvk 4175 Sk cssetk 4183 Ik cidk 4184 |
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-xp 4079 ax-cnv 4080 ax-sset 4082 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-ral 2619 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-cnvk 4186 df-ssetk 4193 df-idk 4195 |
This theorem is referenced by: nnsucelrlem1 4424 nndisjeq 4429 tfinrelkex 4487 oddfinex 4504 evenodddisjlem1 4515 phiexg 4571 opexg 4587 proj1exg 4591 proj2exg 4592 setconslem5 4735 1stex 4739 swapex 4742 |
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