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Theorem relco 4762
Description: A composition is a relation. Exercise 24 of [TakeutiZaring] p. 25. (Contributed by NM, 26-Jan-1997.)
Assertion
Ref Expression
relco  Rel  o.

Proof of Theorem relco
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-co 4297 . 2  o.  { <. , 
>.  |  }
21relopabi 4406 1  Rel  o.
Colors of variables: wff set class
Syntax hints:   wa 97  wex 1378   class class class wbr 3755    o. ccom 4292   Rel wrel 4293
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-14 1402  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-sep 3866  ax-pow 3918  ax-pr 3935
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-rex 2306  df-v 2553  df-un 2916  df-in 2918  df-ss 2925  df-pw 3353  df-sn 3373  df-pr 3374  df-op 3376  df-opab 3810  df-xp 4294  df-rel 4295  df-co 4297
This theorem is referenced by:  dfco2  4763  resco  4768  coiun  4773  cocnvcnv2  4775  cores2  4776  co02  4777  co01  4778  coi1  4779  coass  4782  cossxp  4786  funco  4883  fmptco  5273  cofunexg  5680  dftpos4  5819
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