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Theorem rnco2 5318
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 5317 . 2  |-  ran  ( A  o.  B )  =  ran  ( A  |`  ran  B )
2 df-ima 4832 . 2  |-  ( A
" ran  B )  =  ran  ( A  |`  ran  B )
31, 2eqtr4i 2411 1  |-  ran  ( A  o.  B )  =  ( A " ran  B )
Colors of variables: wff set class
Syntax hints:    = wceq 1649   ran crn 4820    |` cres 4821   "cima 4822    o. ccom 4823
This theorem is referenced by:  dmco  5319  isf34lem7  8193  isf34lem6  8194  imasless  13693  gsumzf1o  15447  gsumzmhm  15461  gsumzinv  15468  dprdf1o  15518  ovolficcss  19234  volsup  19318  uniiccdif  19338  uniioombllem3  19345  dyadmbl  19360  itg1climres  19474  pf1rcl  19837  cvmlift3lem6  24791  volsupnfl  25957
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-14 1721  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2369  ax-sep 4272  ax-nul 4280  ax-pr 4345
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2243  df-mo 2244  df-clab 2375  df-cleq 2381  df-clel 2384  df-nfc 2513  df-ne 2553  df-ral 2655  df-rex 2656  df-rab 2659  df-v 2902  df-dif 3267  df-un 3269  df-in 3271  df-ss 3278  df-nul 3573  df-if 3684  df-sn 3764  df-pr 3765  df-op 3767  df-br 4155  df-opab 4209  df-xp 4825  df-cnv 4827  df-co 4828  df-dm 4829  df-rn 4830  df-res 4831  df-ima 4832
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