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Theorem dfrn2 4469
Description: Alternate definition of range. Definition 4 of [Suppes] p. 60. (Contributed by NM, 27-Dec-1996.)
Assertion
Ref Expression
dfrn2  ran  {  |  }
Distinct variable group:   ,,

Proof of Theorem dfrn2
StepHypRef Expression
1 df-rn 4302 . 2  ran  dom  `'
2 df-dm 4301 . 2  dom  `'  {  |  `' }
3 vex 2557 . . . . 5 
_V
4 vex 2557 . . . . 5 
_V
53, 4brcnv 4464 . . . 4  `'
65exbii 1496 . . 3  `'
76abbii 2153 . 2  {  |  `' }  {  |  }
81, 2, 73eqtri 2064 1  ran  {  |  }
Colors of variables: wff set class
Syntax hints:   wceq 1243  wex 1381   {cab 2026   class class class wbr 3758   `'ccnv 4290   dom cdm 4291   ran crn 4292
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-14 1405  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3869  ax-pow 3921  ax-pr 3938
This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-eu 1903  df-mo 1904  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2556  df-un 2919  df-in 2921  df-ss 2928  df-pw 3356  df-sn 3376  df-pr 3377  df-op 3379  df-br 3759  df-opab 3813  df-cnv 4299  df-dm 4301  df-rn 4302
This theorem is referenced by:  dfrn3  4470  dfdm4  4473  dm0rn0  4498  dmmrnm  4500  dfrnf  4521  dfima2  4616  funcnv3  4907
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