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Theorem rnco2 5196
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 5195 . 2  |-  ran  ( A  o.  B )  =  ran  ( A  |`  ran  B )
2 df-ima 4718 . 2  |-  ( A
" ran  B )  =  ran  ( A  |`  ran  B )
31, 2eqtr4i 2319 1  |-  ran  ( A  o.  B )  =  ( A " ran  B )
Colors of variables: wff set class
Syntax hints:    = wceq 1632   ran crn 4706    |` cres 4707   "cima 4708    o. ccom 4709
This theorem is referenced by:  dmco  5197  isf34lem7  8021  isf34lem6  8022  imasless  13458  gsumzf1o  15212  gsumzmhm  15226  gsumzinv  15233  dprdf1o  15283  ovolficcss  18845  volsup  18929  uniiccdif  18949  uniioombllem3  18956  dyadmbl  18971  itg1climres  19085  pf1rcl  19448  cvmlift3lem6  23870
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-nul 4165  ax-pr 4230
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-mo 2161  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rex 2562  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-br 4040  df-opab 4094  df-xp 4711  df-cnv 4713  df-co 4714  df-dm 4715  df-rn 4716  df-res 4717  df-ima 4718
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