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Theorem rnmpt 4582
 Description: The range of a function in maps-to notation. (Contributed by Scott Fenton, 21-Mar-2011.) (Revised by Mario Carneiro, 31-Aug-2015.)
Hypothesis
Ref Expression
rnmpt.1
Assertion
Ref Expression
rnmpt
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   ()   ()   (,)

Proof of Theorem rnmpt
StepHypRef Expression
1 rnopab 4581 . 2
2 rnmpt.1 . . . 4
3 df-mpt 3820 . . . 4
42, 3eqtri 2060 . . 3
54rneqi 4562 . 2
6 df-rex 2312 . . 3
76abbii 2153 . 2
81, 5, 73eqtr4i 2070 1
 Colors of variables: wff set class Syntax hints:   wa 97   wceq 1243  wex 1381   wcel 1393  cab 2026  wrex 2307  copab 3817   cmpt 3818   crn 4346 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-rex 2312  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-mpt 3820  df-cnv 4353  df-dm 4355  df-rn 4356 This theorem is referenced by:  elrnmpt  4583  elrnmpt1  4585  elrnmptg  4586  dfiun3g  4589  dfiin3g  4590  fnrnfv  5220  fmpt  5319  fnasrn  5341  fnasrng  5343  fliftf  5439  abrexex  5744  abrexexg  5745  fo1st  5784  fo2nd  5785  qliftf  6191
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