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Theorem fvclex 5982
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 5134 . . 3  |-  ran  F  e.  _V
3 p0ex 4387 . . 3  |-  { (/) }  e.  _V
42, 3unex 4708 . 2  |-  ( ran 
F  u.  { (/) } )  e.  _V
5 fvclss 5981 . 2  |-  { y  |  E. x  y  =  ( F `  x ) }  C_  ( ran  F  u.  { (/)
} )
64, 5ssexi 4349 1  |-  { y  |  E. x  y  =  ( F `  x ) }  e.  _V
Colors of variables: wff set class
Syntax hints:   E.wex 1551    = wceq 1653    e. wcel 1726   {cab 2423   _Vcvv 2957    u. cun 3319   (/)c0 3629   {csn 3815   ran crn 4880   ` cfv 5455
This theorem is referenced by:  fvresex  5983
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-13 1728  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418  ax-sep 4331  ax-nul 4339  ax-pow 4378  ax-pr 4404  ax-un 4702
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2286  df-mo 2287  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-ne 2602  df-ral 2711  df-rex 2712  df-rab 2715  df-v 2959  df-sbc 3163  df-dif 3324  df-un 3326  df-in 3328  df-ss 3335  df-nul 3630  df-if 3741  df-pw 3802  df-sn 3821  df-pr 3822  df-op 3824  df-uni 4017  df-br 4214  df-opab 4268  df-cnv 4887  df-dm 4889  df-rn 4890  df-iota 5419  df-fv 5463
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