Theorem disj2

Description: Two ways of saying that two classes are disjoint. (Contributed by NM, 17-May-1998)

	Ref	Expression
Assertion	disj2	$$⊢A\cap B=\varnothing \leftrightarrow A\subseteq \mathrm{V}\setminus B$$

Proof

Step	Hyp	Ref	Expression
1		ssv	$$⊢A\subseteq \mathrm{V}$$
2		reldisj	$$⊢A\subseteq \mathrm{V}\to \left(A\cap B=\varnothing \leftrightarrow A\subseteq \mathrm{V}\setminus B\right)$$
3	1 2	ax-mp	$$⊢A\cap B=\varnothing \leftrightarrow A\subseteq \mathrm{V}\setminus B$$