Theorem difexg

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

	Ref	Expression
Assertion	difexg	|- ( A e. V -> ( A \ B ) e. _V )

Proof

Step	Hyp	Ref	Expression
1		difss	|- ( A \ B ) C_ A
2		ssexg	|- ( ( ( A \ B ) C_ A /\ A e. V ) -> ( A \ B ) e. _V )
3	1 2	mpan	|- ( A e. V -> ( A \ B ) e. _V )