Theorem relopab 5247

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	|- Rel { <. x , y >. | ph }

Proof of Theorem relopab

Step	Hyp	Ref	Expression
1		eqid 2622	. 2 |- { <. x , y >. | ph } = { <. x , y >. | ph }
2	1	relopabi 5245	1 |- Rel { <. x , y >. | ph }

Syntax hints:   {copab 4712   Rel wrel 5119

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3an 1039  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-rab 2921  df-v 3202  df-dif 3577  df-un 3579  df-in 3581  df-ss 3588  df-nul 3916  df-if 4087  df-sn 4178  df-pr 4180  df-op 4184  df-opab 4713  df-xp 5120  df-rel 5121

This theorem is referenced by:  opabid2  5251  inopab  5252  difopab  5253  dfres2  5453  cnvopab  5533  funopab  5923  relmptopab  6883  elopabi  7231  relmpt2opab  7259  shftfn  13813  cicer  16466  joindmss  17007  meetdmss  17021  lgsquadlem3  25107  perpln1  25605  perpln2  25606  fpwrelmapffslem  29507  fpwrelmap  29508  relfae  30310  vvdifopab  34024  inxprnres  34060  prtlem12  34152  dicvalrelN  36474  diclspsn  36483  dih1dimatlem  36618  rfovcnvf1od  38298