Metamath Proof Explorer


Theorem relopab

Description: A class of ordered pairs is a relation. (Contributed by NM, 8-Mar-1995) Remove disjoint variable conditions. (Revised by Alan Sare, 9-Jul-2013) (Proof shortened by Mario Carneiro, 21-Dec-2013)

Ref Expression
Assertion relopab
|- Rel { <. x , y >. | ph }

Proof

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