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Theorem rnco2 5180
Description: The range of the composition of two classes. (Contributed by NM, 27-Mar-2008.)
Assertion
Ref Expression
rnco2  |-  ran  ( A  o.  B )  =  ( A " ran  B )

Proof of Theorem rnco2
StepHypRef Expression
1 rnco 5179 . 2  |-  ran  ( A  o.  B )  =  ran  ( A  |`  ran  B )
2 df-ima 4702 . 2  |-  ( A
" ran  B )  =  ran  ( A  |`  ran  B )
31, 2eqtr4i 2306 1  |-  ran  ( A  o.  B )  =  ( A " ran  B )
Colors of variables: wff set class
Syntax hints:    = wceq 1623   ran crn 4690    |` cres 4691   "cima 4692    o. ccom 4693
This theorem is referenced by:  dmco  5181  isf34lem7  8005  isf34lem6  8006  imasless  13442  gsumzf1o  15196  gsumzmhm  15210  gsumzinv  15217  dprdf1o  15267  ovolficcss  18829  volsup  18913  uniiccdif  18933  uniioombllem3  18940  dyadmbl  18955  itg1climres  19069  pf1rcl  19432  cvmlift3lem6  23855
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-eu 2147  df-mo 2148  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-br 4024  df-opab 4078  df-xp 4695  df-cnv 4697  df-co 4698  df-dm 4699  df-rn 4700  df-res 4701  df-ima 4702
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