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Theorem brelrn 4589
 Description: The second argument of a binary relation belongs to its range. (Contributed by NM, 13-Aug-2004.)
Hypotheses
Ref Expression
brelrn.1
brelrn.2
Assertion
Ref Expression
brelrn

Proof of Theorem brelrn
StepHypRef Expression
1 brelrn.1 . 2
2 brelrn.2 . 2
3 brelrng 4587 . 2
41, 2, 3mp3an12 1259 1
 Colors of variables: wff set class Syntax hints:   wi 4   wcel 1434  cvv 2602   class class class wbr 3787   crn 4366 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-14 1446  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064  ax-sep 3898  ax-pow 3950  ax-pr 3966 This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-eu 1945  df-mo 1946  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-un 2978  df-in 2980  df-ss 2987  df-pw 3386  df-sn 3406  df-pr 3407  df-op 3409  df-br 3788  df-opab 3842  df-cnv 4373  df-dm 4375  df-rn 4376 This theorem is referenced by:  opelrn  4590  dfco2a  4845  cores  4848  dffun9  4954  funcnv  4985  rntpos  5900  tfrexlem  5977
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