Theorem relinxp

Description: Intersection with a Cartesian product is a relation. (Contributed by Peter Mazsa, 4-Mar-2019)

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

Proof

Step	Hyp	Ref	Expression
1		relxp	$$⊢\mathrm{Rel}\left(A\times B\right)$$
2		relin2	$$⊢\mathrm{Rel}\left(A\times B\right)\to \mathrm{Rel}\left(R\cap \left(A\times B\right)\right)$$
3	1 2	ax-mp	$$⊢\mathrm{Rel}\left(R\cap \left(A\times B\right)\right)$$