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Theorem brinxp2 5066
Description: Intersection of binary relation with Cartesian product. (Contributed by NM, 3-Mar-2007.) (Revised by Mario Carneiro, 26-Apr-2015.)
Assertion
Ref Expression
brinxp2

Proof of Theorem brinxp2
StepHypRef Expression
1 brin 4501 . 2
2 ancom 450 . 2
3 brxp 5035 . . . 4
43anbi1i 695 . . 3
5 df-3an 975 . . 3
64, 5bitr4i 252 . 2
71, 2, 63bitri 271 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  /\wa 369  /\w3a 973  e.wcel 1818  i^icin 3474   class class class wbr 4452  X.cxp 5002
This theorem is referenced by:  brinxp  5067  fncnv  5657  erinxp  7404  fpwwe2lem8  9036  fpwwe2lem9  9037  fpwwe2lem12  9040  nqerf  9329  nqerid  9332  isstruct  14642  pwsle  14889  psss  15844  psssdm2  15845  pi1cpbl  21544  pi1grplem  21549
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-opab 4511  df-xp 5010
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