Theorem reldif

Description: A difference cutting down a relation is a relation. (Contributed by NM, 31-Mar-1998)

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

Proof

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