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Theorem brelrng 4593
 Description: The second argument of a binary relation belongs to its range. (Contributed by NM, 29-Jun-2008.)
Assertion
Ref Expression
brelrng

Proof of Theorem brelrng
StepHypRef Expression
1 brcnvg 4544 . . . . 5
21ancoms 264 . . . 4
32biimp3ar 1278 . . 3
4 breldmg 4569 . . . 4
543com12 1143 . . 3
63, 5syld3an3 1215 . 2
7 df-rn 4382 . 2
86, 7syl6eleqr 2173 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 103   w3a 920   wcel 1434   class class class wbr 3793  ccnv 4370   cdm 4371   crn 4372 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 3904  ax-pow 3956  ax-pr 3972 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 3392  df-sn 3412  df-pr 3413  df-op 3415  df-br 3794  df-opab 3848  df-cnv 4379  df-dm 4381  df-rn 4382 This theorem is referenced by:  opelrng  4594  brelrn  4595  relelrn  4598  fvssunirng  5221  shftfvalg  9844  ovshftex  9845  shftfval  9847
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