Theorem relopab 5134

Description: A class of ordered pairs is a relation. (Contributed by NM, 8-Mar-1995.) (Unnecessary distinct variable restrictions were removed by Alan Sare, 9-Jul-2013.) (Proof shortened by Mario Carneiro, 21-Dec-2013.)

Assertion

Ref	Expression
relopab

Proof of Theorem relopab

Step	Hyp	Ref	Expression
1		eqid 2457	. 2
2	1	relopabi 5133	1

Syntax hints:  {copab 4509  Relwrel 5009

This theorem is referenced by:  opabid2  5137  inopab  5138  difopab  5139  dfres2  5331  cnvopab  5412  funopab  5626  relmptopab  6523  elopabi  6861  relmpt2opab  6882  shftfn  12906  joindmss  15637  meetdmss  15651  eltopspOLD  19419  lgsquadlem3  23631  perpln1  24087  perpln2  24088  fpwrelmapffslem  27555  fpwrelmap  27556  relfae  28219  prtlem12  30608  cicer  32590  dicvalrelN  36912  diclspsn  36921  dih1dimatlem  37056

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-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-opab 4511  df-xp 5010  df-rel 5011