Theorem dfrel4v 5463

Description: A relation can be expressed as the set of ordered pairs in it. An analogue of dffn5 5918 for relations. (Contributed by Mario Carneiro, 16-Aug-2015.)

Assertion

Ref	Expression
dfrel4v

Distinct variable group:   ,,

Proof of Theorem dfrel4v

Step	Hyp	Ref	Expression
1		dfrel2 5462	. 2
2		eqcom 2466	. 2
3		cnvcnv3 5461	. . 3
4	3	eqeq2i 2475	. 2
5	1, 2, 4	3bitri 271	1

Syntax hints:  <->wb 184  =wceq 1395   class class class wbr 4452  {copab 4509  `'ccnv 5003  Relwrel 5009

This theorem is referenced by:  dffn5  5918  fsplit  6905  pwsle  14889  tgphaus  20615  dfrel4  27454  fneer  30171  dfafn5a  32245

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-ral 2812  df-rex 2813  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-xp 5010  df-rel 5011  df-cnv 5012