Theorem disjdif

Description: A class and its relative complement are disjoint. Theorem 38 of Suppes p. 29. (Contributed by NM, 24-Mar-1998)

	Ref	Expression
Assertion	disjdif	$$⊢A\cap \left(B\setminus A\right)=\varnothing$$

Proof

Step	Hyp	Ref	Expression
1		ssid	$$⊢A\subseteq A$$
2		disjdifg	$$⊢A\subseteq A\to A\cap \left(B\setminus A\right)=\varnothing$$
3	1 2	ax-mp	$$⊢A\cap \left(B\setminus A\right)=\varnothing$$