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Mirrors > Home > NFE Home > Th. List > inex | Unicode version |
Description: The intersection of two sets is a set. (Contributed by SF, 12-Jan-2015.) |
Ref | Expression |
---|---|
boolex.1 | |
boolex.2 |
Ref | Expression |
---|---|
inex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | boolex.1 | . 2 | |
2 | boolex.2 | . 2 | |
3 | inexg 4100 | . 2 | |
4 | 1, 2, 3 | mp2an 653 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wcel 1710 cvv 2859 cin 3208 |
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 |
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-v 2861 df-nin 3211 df-compl 3212 df-in 3213 |
This theorem is referenced by: cnvkexg 4286 ssetkex 4294 sikexg 4296 ins2kexg 4305 ins3kexg 4306 idkex 4314 addcexlem 4382 nnsucelrlem1 4424 nndisjeq 4429 preaddccan2lem1 4454 ltfinex 4464 ssfin 4470 ncfinraiselem2 4480 ncfinlowerlem1 4482 tfinrelkex 4487 evenfinex 4503 oddfinex 4504 evenodddisjlem1 4515 nnadjoinlem1 4519 nnpweqlem1 4522 srelkex 4525 sfintfinlem1 4531 tfinnnlem1 4533 spfinex 4537 phiexg 4571 opexg 4587 proj1exg 4591 proj2exg 4592 phialllem1 4616 phialllem2 4617 setconslem5 4735 1stex 4739 swapex 4742 ssetex 4744 imaexg 4746 coexg 4749 siexg 4752 idex 5504 mptexlem 5810 composeex 5820 addcfnex 5824 funsex 5828 fnsex 5832 crossex 5850 domfnex 5870 ranfnex 5871 clos1ex 5876 transex 5910 refex 5911 antisymex 5912 connexex 5913 foundex 5914 extex 5915 symex 5916 partialex 5917 strictex 5918 weex 5919 erex 5920 mapexi 6003 fnpm 6008 enpw1lem1 6061 enmap2lem1 6063 enmap1lem1 6069 nenpw1pwlem1 6084 ovmuc 6130 mucex 6133 ovcelem1 6171 ceex 6174 sbthlem1 6203 tcfnex 6244 nmembers1lem1 6268 nncdiv3lem2 6276 nnc3n3p1 6278 spacvallem1 6281 nchoicelem11 6299 nchoicelem18 6306 |
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