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Theorem fvclex 5761
Description: Existence of the class of values of a set. (Contributed by NM, 9-Nov-1995.)
Hypothesis
Ref Expression
fvclex.1  |-  F  e. 
_V
Assertion
Ref Expression
fvclex  |-  { y  |  E. x  y  =  ( F `  x ) }  e.  _V
Distinct variable group:    x, y, F

Proof of Theorem fvclex
StepHypRef Expression
1 fvclex.1 . . . 4  |-  F  e. 
_V
21rnex 4942 . . 3  |-  ran  F  e.  _V
3 p0ex 4197 . . 3  |-  { (/) }  e.  _V
42, 3unex 4518 . 2  |-  ( ran 
F  u.  { (/) } )  e.  _V
5 fvclss 5760 . 2  |-  { y  |  E. x  y  =  ( F `  x ) }  C_  ( ran  F  u.  { (/)
} )
64, 5ssexi 4159 1  |-  { y  |  E. x  y  =  ( F `  x ) }  e.  _V
Colors of variables: wff set class
Syntax hints:   E.wex 1528    = wceq 1623    e. wcel 1684   {cab 2269   _Vcvv 2788    u. cun 3150   (/)c0 3455   {csn 3640   ran crn 4690   ` cfv 5255
This theorem is referenced by:  fvresex  5762
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-13 1686  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pow 4188  ax-pr 4214  ax-un 4512
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-sbc 2992  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-pw 3627  df-sn 3646  df-pr 3647  df-op 3649  df-uni 3828  df-br 4024  df-opab 4078  df-cnv 4697  df-dm 4699  df-rn 4700  df-iota 5219  df-fv 5263
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