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Theorem brelrn 4510
Description: The second argument of a binary relation belongs to its range. (Contributed by NM, 13-Aug-2004.)
Hypotheses
Ref Expression
brelrn.1  _V
brelrn.2  _V
Assertion
Ref Expression
brelrn  C  ran  C

Proof of Theorem brelrn
StepHypRef Expression
1 brelrn.1 . 2  _V
2 brelrn.2 . 2  _V
3 brelrng 4508 . 2  _V  _V  C  ran  C
41, 2, 3mp3an12 1221 1  C  ran  C
Colors of variables: wff set class
Syntax hints:   wi 4   wcel 1390   _Vcvv 2551   class class class wbr 3755   ran crn 4289
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-14 1402  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-sep 3866  ax-pow 3918  ax-pr 3935
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-eu 1900  df-mo 1901  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-un 2916  df-in 2918  df-ss 2925  df-pw 3353  df-sn 3373  df-pr 3374  df-op 3376  df-br 3756  df-opab 3810  df-cnv 4296  df-dm 4298  df-rn 4299
This theorem is referenced by:  opelrn  4511  dfco2a  4764  cores  4767  dffun9  4873  funcnv  4903  rntpos  5813  tfrexlem  5889
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