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Theorem relco 5510
Description: A composition is a relation. Exercise 24 of [TakeutiZaring] p. 25. (Contributed by NM, 26-Jan-1997.)
Assertion
Ref Expression
relco

Proof of Theorem relco
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-co 5013 . 2
21relopabi 5133 1
Colors of variables: wff setvar class
Syntax hints:  /\wa 369  E.wex 1612   class class class wbr 4452  o.ccom 5008  Relwrel 5009
This theorem is referenced by:  dfco2  5511  resco  5516  coeq0  5521  coiun  5522  cocnvcnv2  5524  cores2  5525  co02  5526  co01  5527  coi1  5528  coass  5531  cossxp  5535  fmptco  6064  cofunexg  6764  dftpos4  6993  wunco  9132  imasless  14937  znleval  18593  metustexhalfOLD  21066  metustexhalf  21067  fcoinver  27460  fmptcof2  27502  dfpo2  29184  cnvco1  29189  cnvco2  29190  opelco3  29208  txpss3v  29528  sscoid  29563  sblpnf  31190
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-opab 4511  df-xp 5010  df-rel 5011  df-co 5013
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