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Theorem afvelrnb0 38811
 Description: A member of a function's range is a value of the function, only one direction of implication of fvelrnb 5926. (Contributed by Alexander van der Vekens, 1-Jun-2017.)
Assertion
Ref Expression
afvelrnb0 '''
Distinct variable groups:   ,   ,   ,

Proof of Theorem afvelrnb0
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 fnrnafv 38809 . . 3 '''
21eleq2d 2534 . 2 '''
3 eqeq1 2475 . . . . . 6 ''' '''
4 eqcom 2478 . . . . . 6 ''' '''
53, 4syl6bb 269 . . . . 5 ''' '''
65rexbidv 2892 . . . 4 ''' '''
76elabg 3174 . . 3 ''' ''' '''
87ibi 249 . 2 ''' '''
92, 8syl6bi 236 1 '''
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1452   wcel 1904  cab 2457  wrex 2757   crn 4840   wfn 5584  '''cafv 38760 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-9 1913  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451  ax-sep 4518  ax-nul 4527  ax-pr 4639 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-eu 2323  df-mo 2324  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ne 2643  df-ral 2761  df-rex 2762  df-rab 2765  df-v 3033  df-sbc 3256  df-dif 3393  df-un 3395  df-in 3397  df-ss 3404  df-nul 3723  df-if 3873  df-sn 3960  df-pr 3962  df-op 3966  df-uni 4191  df-br 4396  df-opab 4455  df-mpt 4456  df-id 4754  df-xp 4845  df-rel 4846  df-cnv 4847  df-co 4848  df-dm 4849  df-rn 4850  df-res 4851  df-iota 5553  df-fun 5591  df-fn 5592  df-fv 5597  df-dfat 38762  df-afv 38763 This theorem is referenced by:  ffnafv  38818
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