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Theorem rnco2 5369
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 5368 . 2  |-  ran  ( A  o.  B )  =  ran  ( A  |`  ran  B )
2 df-ima 4883 . 2  |-  ( A
" ran  B )  =  ran  ( A  |`  ran  B )
31, 2eqtr4i 2458 1  |-  ran  ( A  o.  B )  =  ( A " ran  B )
Colors of variables: wff set class
Syntax hints:    = wceq 1652   ran crn 4871    |` cres 4872   "cima 4873    o. ccom 4874
This theorem is referenced by:  dmco  5370  isf34lem7  8251  isf34lem6  8252  imasless  13757  gsumzf1o  15511  gsumzmhm  15525  gsumzinv  15532  dprdf1o  15582  ovolficcss  19358  volsup  19442  uniiccdif  19462  uniioombllem3  19469  dyadmbl  19484  itg1climres  19598  pf1rcl  19961  cvmlift3lem6  25003  mblfinlem  26234  volsupnfl  26241
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-br 4205  df-opab 4259  df-xp 4876  df-cnv 4878  df-co 4879  df-dm 4880  df-rn 4881  df-res 4882  df-ima 4883
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