Theorem relxp

Description: A Cartesian product is a relation. Theorem 3.13(i) of Monk1 p. 37. (Contributed by NM, 2-Aug-1994)

	Ref	Expression
Assertion	relxp	$$⊢\mathrm{Rel}\left(A\times B\right)$$

Proof

Step	Hyp	Ref	Expression
1		xpss	$$⊢A\times B\subseteq \mathrm{V}\times \mathrm{V}$$
2		df-rel	$$⊢\mathrm{Rel}\left(A\times B\right)\leftrightarrow A\times B\subseteq \mathrm{V}\times \mathrm{V}$$
3	1 2	mpbir	$$⊢\mathrm{Rel}\left(A\times B\right)$$