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Theorem relco 5171
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
Dummy variables  x  y  z are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-co 4698 . 2  |-  ( A  o.  B )  =  { <. x ,  y
>.  |  E. z
( x B z  /\  z A y ) }
21relopabi 4811 1  |-  Rel  ( A  o.  B )
Colors of variables: wff set class
Syntax hints:    /\ wa 358   E.wex 1528   class class class wbr 4023    o. ccom 4693   Rel wrel 4694
This theorem is referenced by:  dfco2  5172  resco  5177  coiun  5182  cocnvcnv2  5184  cores2  5185  co02  5186  co01  5187  coi1  5188  coass  5191  cossxp  5195  coexg  5215  fmptco  5691  cofunexg  5739  dftpos4  6253  wunco  8355  imasless  13442  znleval  16508  dfpo2  23523  cnvco1  23528  cnvco2  23529  txpss3v  23829  dffun10  23864  coeq0  26243  sblpnf  26951
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-opab 4078  df-xp 4695  df-rel 4696  df-co 4698
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