Metamath Proof Explorer


Theorem pwvrel

Description: A set is a binary relation if and only if it belongs to the powerclass of the cartesian square of the universal class. (Contributed by Peter Mazsa, 14-Jun-2018) (Revised by BJ, 16-Dec-2023)

Ref Expression
Assertion pwvrel A V A 𝒫 V × V Rel A

Proof

Step Hyp Ref Expression
1 elpwg A V A 𝒫 V × V A V × V
2 df-rel Rel A A V × V
3 1 2 bitr4di A V A 𝒫 V × V Rel A