Theorem relin2

Description: The intersection with a relation is a relation. (Contributed by NM, 17-Jan-2006)

	Ref	Expression
Assertion	relin2	$$⊢\mathrm{Rel}B\to \mathrm{Rel}\left(A\cap B\right)$$

Proof

Step	Hyp	Ref	Expression
1		inss2	$$⊢A\cap B\subseteq B$$
2		relss	$$⊢A\cap B\subseteq B\to \left(\mathrm{Rel}B\to \mathrm{Rel}\left(A\cap B\right)\right)$$
3	1 2	ax-mp	$$⊢\mathrm{Rel}B\to \mathrm{Rel}\left(A\cap B\right)$$