Theorem difexg

Description: Existence of a difference. (Contributed by NM, 26-May-1998)

	Ref	Expression
Assertion	difexg	$$⊢A\in V\to A\setminus B\in \mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		difss	$$⊢A\setminus B\subseteq A$$
2		ssexg	$$⊢\left(A\setminus B\subseteq A\wedge A\in V\right)\to A\setminus B\in \mathrm{V}$$
3	1 2	mpan	$$⊢A\in V\to A\setminus B\in \mathrm{V}$$