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Theorem fvclex 6767
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 6729 . . 3  |-  ran  F  e.  _V
3 p0ex 4640 . . 3  |-  { (/) }  e.  _V
42, 3unex 6593 . 2  |-  ( ran 
F  u.  { (/) } )  e.  _V
5 fvclss 6153 . 2  |-  { y  |  E. x  y  =  ( F `  x ) }  C_  ( ran  F  u.  { (/)
} )
64, 5ssexi 4598 1  |-  { y  |  E. x  y  =  ( F `  x ) }  e.  _V
Colors of variables: wff setvar class
Syntax hints:    = wceq 1379   E.wex 1596    e. wcel 1767   {cab 2452   _Vcvv 3118    u. cun 3479   (/)c0 3790   {csn 4033   ran crn 5006   ` cfv 5594
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-8 1769  ax-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-sep 4574  ax-nul 4582  ax-pow 4631  ax-pr 4692  ax-un 6587
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-eu 2279  df-mo 2280  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-ral 2822  df-rex 2823  df-rab 2826  df-v 3120  df-sbc 3337  df-dif 3484  df-un 3486  df-in 3488  df-ss 3495  df-nul 3791  df-if 3946  df-pw 4018  df-sn 4034  df-pr 4036  df-op 4040  df-uni 4252  df-br 4454  df-opab 4512  df-cnv 5013  df-dm 5015  df-rn 5016  df-iota 5557  df-fv 5602
This theorem is referenced by:  fvresex  6768
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