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Theorem rnmpt 4782
 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 4781 . 2
2 rnmpt.1 . . . 4
3 df-mpt 3986 . . . 4
42, 3eqtri 2158 . . 3
54rneqi 4762 . 2
6 df-rex 2420 . . 3
76abbii 2253 . 2
81, 5, 73eqtr4i 2168 1
 Colors of variables: wff set class Syntax hints:   wa 103   wceq 1331  wex 1468   wcel 1480  cab 2123  wrex 2415  copab 3983   cmpt 3984   crn 4535 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-rex 2420  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-mpt 3986  df-cnv 4542  df-dm 4544  df-rn 4545 This theorem is referenced by:  elrnmpt  4783  elrnmpt1  4785  elrnmptg  4786  dfiun3g  4791  dfiin3g  4792  fnrnfv  5461  fmpt  5563  fnasrn  5591  fnasrng  5593  fliftf  5693  abrexex  6008  abrexexg  6009  fo1st  6048  fo2nd  6049  qliftf  6507  negfi  10992  restco  12332
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