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Theorem rnoprab 5587
 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 5552 . . 3
21rneqi 4562 . 2
3 rnopab 4581 . 2
4 exrot3 1580 . . . 4
5 vex 2560 . . . . . . . 8
6 vex 2560 . . . . . . . 8
75, 6opex 3966 . . . . . . 7
87isseti 2563 . . . . . 6
9 19.41v 1782 . . . . . 6
108, 9mpbiran 847 . . . . 5
11102exbii 1497 . . . 4
124, 11bitri 173 . . 3
1312abbii 2153 . 2
142, 3, 133eqtri 2064 1
 Colors of variables: wff set class Syntax hints:   wa 97   wceq 1243  wex 1381  cab 2026  cop 3378  copab 3817   crn 4346  coprab 5513 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 3875  ax-pow 3927  ax-pr 3944 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 2559  df-un 2922  df-in 2924  df-ss 2931  df-pw 3361  df-sn 3381  df-pr 3382  df-op 3384  df-br 3765  df-opab 3819  df-cnv 4353  df-dm 4355  df-rn 4356  df-oprab 5516 This theorem is referenced by:  rnoprab2  5588
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