Metamath Proof Explorer


Theorem reldvds

Description: The divides relation is in fact a relation. (Contributed by Steve Rodriguez, 20-Jan-2020)

Ref Expression
Assertion reldvds
|- Rel ||

Proof

Step Hyp Ref Expression
1 df-dvds
 |-  || = { <. x , y >. | ( ( x e. ZZ /\ y e. ZZ ) /\ E. z e. ZZ ( z x. x ) = y ) }
2 1 relopabiv
 |-  Rel ||