Theorem relinxp

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

	Ref	Expression
Assertion	relinxp	⊢ Rel ( 𝑅 ∩ ( 𝐴 × 𝐵 ) )

Proof

Step	Hyp	Ref	Expression
1		relxp	⊢ Rel ( 𝐴 × 𝐵 )
2		relin2	⊢ ( Rel ( 𝐴 × 𝐵 ) → Rel ( 𝑅 ∩ ( 𝐴 × 𝐵 ) ) )
3	1 2	ax-mp	⊢ Rel ( 𝑅 ∩ ( 𝐴 × 𝐵 ) )