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Mirrors > Home > NFE Home > Th. List > brin | Unicode version |
Description: The intersection of two relations. (Contributed by FL, 7-Oct-2008.) |
Ref | Expression |
---|---|
brin |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elin 3219 | . 2 | |
2 | df-br 4640 | . 2 | |
3 | df-br 4640 | . . 3 | |
4 | df-br 4640 | . . 3 | |
5 | 3, 4 | anbi12i 678 | . 2 |
6 | 1, 2, 5 | 3bitr4i 268 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 176 wa 358 wcel 1710 cin 3208 cop 4561 class class class wbr 4639 |
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 |
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 df-br 4640 |
This theorem is referenced by: brinxp2 4835 brres 4949 intasym 5028 fncnv 5158 dfid4 5503 trtxp 5781 brtxp 5783 elfix 5787 ersymtr 5932 porta 5933 sopc 5934 weds 5938 enpw1lem1 6061 enmap2lem1 6063 enmap1lem1 6069 nchoicelem8 6296 nchoicelem19 6307 |
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