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Theorem elrnmpti 4800
 Description: Membership in the range of a function. (Contributed by NM, 30-Aug-2004.) (Revised by Mario Carneiro, 31-Aug-2015.)
Hypotheses
Ref Expression
rnmpt.1
elrnmpti.2
Assertion
Ref Expression
elrnmpti
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem elrnmpti
StepHypRef Expression
1 elrnmpti.2 . . 3
21rgenw 2490 . 2
3 rnmpt.1 . . 3
43elrnmptg 4799 . 2
52, 4ax-mp 5 1
 Colors of variables: wff set class Syntax hints:   wb 104   wceq 1332   wcel 1481  wral 2417  wrex 2418  cvv 2689   cmpt 3997   crn 4548 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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-14 1493  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122  ax-sep 4054  ax-pow 4106  ax-pr 4139 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1737  df-eu 2003  df-mo 2004  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ral 2422  df-rex 2423  df-v 2691  df-un 3080  df-in 3082  df-ss 3089  df-pw 3517  df-sn 3538  df-pr 3539  df-op 3541  df-br 3938  df-opab 3998  df-mpt 3999  df-cnv 4555  df-dm 4557  df-rn 4558 This theorem is referenced by:  elrest  12167
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