Theorem rnex 3361

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.

Hypothesis

Ref	Expression
dmex.1	|- A e. V

Assertion

Ref	Expression
rnex	|- ran A e. V

Proof of Theorem rnex

Step	Hyp	Ref	Expression
1		dmex.1	. 2 |- A e. V
2		rnexg 3359	. 2 |- (A e. V -> ran A e. V)
3	1, 2	ax-mp 7	1 |- ran A e. V

Syntax hints:   e. wcel 958  Vcvv 1811  ran crn 3171

This theorem is referenced by:  elxp4 3453  elxp5 3454  ffoss 3711  fvclex 3856  2ndval 4082  fo2nd 4092  xpmapenlem2 4497  aceq3lem 4732  aceq5 4740  ac6lem 4754  fodom 4798  infxpidmlem8 7559  retopbas 7655  bafval 8223  0vfval 8225  vsfval 8254

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-11 967  ax-12 968  ax-13 969  ax-14 970  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218  ax-ext 1459  ax-sep 2703  ax-pow 2742  ax-pr 2779  ax-un 2866

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 981  df-sb 1172  df-eu 1382  df-mo 1383  df-clab 1464  df-cleq 1469  df-clel 1472  df-ne 1587  df-v 1812  df-dif 2049  df-un 2050  df-in 2051  df-ss 2053  df-nul 2281  df-pw 2402  df-sn 2412  df-pr 2413  df-op 2416  df-uni 2504  df-br 2620  df-opab 2667  df-cnv 3186  df-dm 3188  df-rn 3189

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