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Mirrors > Home > ILE Home > Th. List > brinxp2 | Unicode version |
Description: Intersection of binary relation with Cartesian product. (Contributed by NM, 3-Mar-2007.) (Revised by Mario Carneiro, 26-Apr-2015.) |
Ref | Expression |
---|---|
brinxp2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | brin 4018 | . 2 | |
2 | ancom 264 | . 2 | |
3 | brxp 4619 | . . . 4 | |
4 | 3 | anbi1i 454 | . . 3 |
5 | df-3an 965 | . . 3 | |
6 | 4, 5 | bitr4i 186 | . 2 |
7 | 1, 2, 6 | 3bitri 205 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 w3a 963 wcel 2128 cin 3101 class class class wbr 3967 cxp 4586 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4084 ax-pow 4137 ax-pr 4171 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-pw 3546 df-sn 3567 df-pr 3568 df-op 3570 df-br 3968 df-opab 4028 df-xp 4594 |
This theorem is referenced by: brinxp 4656 fncnv 5238 erinxp 6556 isstructim 12274 isstructr 12275 |
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