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Theorem fnafvelrn 28023
Description: A function's value belongs to its range, analogous to fnfvelrn 5870. (Contributed by Alexander van der Vekens, 25-May-2017.)
Assertion
Ref Expression
fnafvelrn  |-  ( ( F  Fn  A  /\  B  e.  A )  ->  ( F''' B )  e.  ran  F )

Proof of Theorem fnafvelrn
StepHypRef Expression
1 afvelrn 28022 . 2  |-  ( ( Fun  F  /\  B  e.  dom  F )  -> 
( F''' B )  e.  ran  F )
21funfni 5548 1  |-  ( ( F  Fn  A  /\  B  e.  A )  ->  ( F''' B )  e.  ran  F )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 360    e. wcel 1726   ran crn 4882    Fn wfn 5452  '''cafv 27962
This theorem is referenced by:  fafvelrn  28024
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4333  ax-nul 4341  ax-pr 4406
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 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-sbc 3164  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4216  df-opab 4270  df-id 4501  df-xp 4887  df-rel 4888  df-cnv 4889  df-co 4890  df-dm 4891  df-rn 4892  df-res 4893  df-iota 5421  df-fun 5459  df-fn 5460  df-fv 5465  df-dfat 27964  df-afv 27965
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