Theorem brelrn 5238

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

Step	Hyp	Ref	Expression
1		brelrn.1	. 2
2		brelrn.2	. 2
3		brelrng 5237	. 2
4	1, 2, 3	mp3an12 1314	1

Syntax hints:  ->wi 4  e.wcel 1818  cvv 3109   class class class wbr 4452  rancrn 5005

This theorem is referenced by:  opelrn  5239  dfco2a  5512  cores  5515  dffun9  5621  funcnv  5653  rntpos  6987  aceq3lem  8522  axdclem  8920  axdclem2  8921  shftfval  12903  psdmrn  15837  metustexhalfOLD  21066  metustexhalf  21067  itg1addlem4  22106  cotr2g  37786

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-opab 4511  df-cnv 5012  df-dm 5014  df-rn 5015