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Theorem relco 5077
Description: A composition is a relation. Exercise 24 of [TakeutiZaring] p. 25. (Contributed by NM, 26-Jan-1997.)
Assertion
Ref Expression
relco  |-  Rel  ( A  o.  B )

Proof of Theorem relco
StepHypRef Expression
1 df-co 4597 . 2  |-  ( A  o.  B )  =  { <. x ,  y
>.  |  E. z
( x B z  /\  z A y ) }
21relopabi 4718 1  |-  Rel  ( A  o.  B )
Colors of variables: wff set class
Syntax hints:    /\ wa 360   E.wex 1537   class class class wbr 3920    o. ccom 4584   Rel wrel 4585
This theorem is referenced by:  dfco2  5078  resco  5083  coiun  5088  cocnvcnv2  5090  cores2  5091  co02  5092  co01  5093  coi1  5094  coass  5097  cossxp  5101  coexg  5121  fmptco  5543  cofunexg  5591  dftpos4  6105  wunco  8235  imasless  13316  znleval  16340  dfpo2  23282  cnvco1  23287  cnvco2  23288  txpss3v  23593  coeq0  25997  sblpnf  26705
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-14 1626  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234  ax-sep 4038  ax-nul 4046  ax-pr 4108
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 941  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-ne 2414  df-ral 2513  df-rex 2514  df-rab 2516  df-v 2729  df-dif 3081  df-un 3083  df-in 3085  df-ss 3089  df-nul 3363  df-if 3471  df-sn 3550  df-pr 3551  df-op 3553  df-opab 3975  df-xp 4594  df-rel 4595  df-co 4597
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