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Theorem relco 5144
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 4664 . 2  |-  ( A  o.  B )  =  { <. x ,  y
>.  |  E. z
( x B z  /\  z A y ) }
21relopabi 4785 1  |-  Rel  ( A  o.  B )
Colors of variables: wff set class
Syntax hints:    /\ wa 360   E.wex 1537   class class class wbr 3983    o. ccom 4651   Rel wrel 4652
This theorem is referenced by:  dfco2  5145  resco  5150  coiun  5155  cocnvcnv2  5157  cores2  5158  co02  5159  co01  5160  coi1  5161  coass  5164  cossxp  5168  coexg  5188  fmptco  5611  cofunexg  5659  dftpos4  6173  wunco  8309  imasless  13390  znleval  16456  dfpo2  23469  cnvco1  23474  cnvco2  23475  txpss3v  23780  coeq0  26184  sblpnf  26892
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 1927  ax-ext 2237  ax-sep 4101  ax-nul 4109  ax-pr 4172
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 1884  df-clab 2243  df-cleq 2249  df-clel 2252  df-nfc 2381  df-ne 2421  df-ral 2521  df-rex 2522  df-rab 2525  df-v 2759  df-dif 3116  df-un 3118  df-in 3120  df-ss 3127  df-nul 3417  df-if 3526  df-sn 3606  df-pr 3607  df-op 3609  df-opab 4038  df-xp 4661  df-rel 4662  df-co 4664
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