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Theorem rnoprab 5847
 Description: The range of an operation class abstraction. (Contributed by NM, 30-Aug-2004.) (Revised by David Abernethy, 19-Apr-2013.)
Assertion
Ref Expression
rnoprab
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,,)

Proof of Theorem rnoprab
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfoprab2 5811 . . 3
21rneqi 4762 . 2
3 rnopab 4781 . 2
4 exrot3 1668 . . . 4
5 vex 2684 . . . . . . . 8
6 vex 2684 . . . . . . . 8
75, 6opex 4146 . . . . . . 7
87isseti 2689 . . . . . 6
9 19.41v 1874 . . . . . 6
108, 9mpbiran 924 . . . . 5
11102exbii 1585 . . . 4
124, 11bitri 183 . . 3
1312abbii 2253 . 2
142, 3, 133eqtri 2162 1
 Colors of variables: wff set class Syntax hints:   wa 103   wceq 1331  wex 1468  cab 2123  cop 3525  copab 3983   crn 4535  coprab 5768 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-14 1492  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119  ax-sep 4041  ax-pow 4093  ax-pr 4126 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-eu 2000  df-mo 2001  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-v 2683  df-un 3070  df-in 3072  df-ss 3079  df-pw 3507  df-sn 3528  df-pr 3529  df-op 3531  df-br 3925  df-opab 3985  df-cnv 4542  df-dm 4544  df-rn 4545  df-oprab 5771 This theorem is referenced by:  rnoprab2  5848
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