Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > brinxp2 | Structured version Visualization version 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 4704 | . 2 | |
2 | ancom 466 | . 2 | |
3 | brxp 5147 | . . . 4 | |
4 | 3 | anbi1i 731 | . . 3 |
5 | df-3an 1039 | . . 3 | |
6 | 4, 5 | bitr4i 267 | . 2 |
7 | 1, 2, 6 | 3bitri 286 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wa 384 w3a 1037 wcel 1990 cin 3573 class class class wbr 4653 cxp 5112 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-br 4654 df-opab 4713 df-xp 5120 |
This theorem is referenced by: brinxp 5181 fncnv 5962 erinxp 7821 fpwwe2lem8 9459 fpwwe2lem9 9460 fpwwe2lem12 9463 nqerf 9752 nqerid 9755 isstruct 15870 pwsle 16152 psss 17214 psssdm2 17215 pi1cpbl 22844 pi1grplem 22849 |
Copyright terms: Public domain | W3C validator |