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Theorem chfnrn 5424
 Description: The range of a choice function (a function that chooses an element from each member of its domain) is included in the union of its domain. (Contributed by NM, 31-Aug-1999.)
Assertion
Ref Expression
chfnrn
Distinct variable groups:   ,   ,

Proof of Theorem chfnrn
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 fvelrnb 5365 . . . . 5
21biimpd 143 . . . 4
3 eleq1 2151 . . . . . . 7
43biimpcd 158 . . . . . 6
54ralimi 2439 . . . . 5
6 rexim 2468 . . . . 5
75, 6syl 14 . . . 4
82, 7sylan9 402 . . 3
9 eluni2 3663 . . 3
108, 9syl6ibr 161 . 2
1110ssrdv 3032 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wceq 1290   wcel 1439  wral 2360  wrex 2361   wss 3000  cuni 3659   crn 4453   wfn 5023  cfv 5028 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-14 1451  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071  ax-sep 3963  ax-pow 4015  ax-pr 4045 This theorem depends on definitions:  df-bi 116  df-3an 927  df-tru 1293  df-nf 1396  df-sb 1694  df-eu 1952  df-mo 1953  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-ral 2365  df-rex 2366  df-v 2622  df-sbc 2842  df-un 3004  df-in 3006  df-ss 3013  df-pw 3435  df-sn 3456  df-pr 3457  df-op 3459  df-uni 3660  df-br 3852  df-opab 3906  df-mpt 3907  df-id 4129  df-xp 4458  df-rel 4459  df-cnv 4460  df-co 4461  df-dm 4462  df-rn 4463  df-iota 4993  df-fun 5030  df-fn 5031  df-fv 5036 This theorem is referenced by: (None)
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