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Theorem afvelrnb0 28004
 Description: A member of a function's range is a value of the function, only one direction of implication of fvelrnb 5774. (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 28002 . . 3 '''
21eleq2d 2503 . 2 '''
3 eqeq1 2442 . . . . . 6 ''' '''
4 eqcom 2438 . . . . . 6 ''' '''
53, 4syl6bb 253 . . . . 5 ''' '''
65rexbidv 2726 . . . 4 ''' '''
76elabg 3083 . . 3 ''' ''' '''
87ibi 233 . 2 ''' '''
92, 8syl6bi 220 1 '''
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652   wcel 1725  cab 2422  wrex 2706   crn 4879   wfn 5449  '''cafv 27948 This theorem is referenced by:  ffnafv  28011 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-sbc 3162  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-br 4213  df-opab 4267  df-mpt 4268  df-id 4498  df-xp 4884  df-rel 4885  df-cnv 4886  df-co 4887  df-dm 4888  df-rn 4889  df-res 4890  df-iota 5418  df-fun 5456  df-fn 5457  df-fv 5462  df-dfat 27950  df-afv 27951
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