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Theorem rnex 4621
Description: The range of a set is a set. Corollary 6.8(3) of [TakeutiZaring] p. 26. Similar to Lemma 3D of [Enderton] p. 41. (Contributed by NM, 7-Jul-2008.)
Hypothesis
Ref Expression
dmex.1  |-  A  e. 
_V
Assertion
Ref Expression
rnex  |-  ran  A  e.  _V

Proof of Theorem rnex
StepHypRef Expression
1 dmex.1 . 2  |-  A  e. 
_V
2 rnexg 4619 . 2  |-  ( A  e.  _V  ->  ran  A  e.  _V )
31, 2ax-mp 7 1  |-  ran  A  e.  _V
Colors of variables: wff set class
Syntax hints:    e. wcel 1434   _Vcvv 2602   ran crn 4366
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-13 1445  ax-14 1446  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064  ax-sep 3898  ax-pow 3950  ax-pr 3966  ax-un 4190
This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-eu 1945  df-mo 1946  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-rex 2355  df-v 2604  df-un 2978  df-in 2980  df-ss 2987  df-pw 3386  df-sn 3406  df-pr 3407  df-op 3409  df-uni 3604  df-br 3788  df-opab 3842  df-cnv 4373  df-dm 4375  df-rn 4376
This theorem is referenced by:  ffoss  5183  abrexex  5769  fo2nd  5810  tfrexlem  5977  bren  6287  xpassen  6364  iseqex  9512  shftfval  9836
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