Theorem eldifi

Description: Implication of membership in a class difference. (Contributed by NM, 29-Apr-1994)

	Ref	Expression
Assertion	eldifi	$$⊢A\in \left(B\setminus C\right)\to A\in B$$

Proof

Step	Hyp	Ref	Expression
1		eldif	$$⊢A\in \left(B\setminus C\right)\leftrightarrow \left(A\in B\wedge \neg A\in C\right)$$
2	1	simplbi	$$⊢A\in \left(B\setminus C\right)\to A\in B$$