Theorem nelneq2

Description: A way of showing two classes are not equal. (Contributed by NM, 12-Jan-2002)

	Ref	Expression
Assertion	nelneq2	$$⊢\left(A\in B\wedge \neg A\in C\right)\to \neg B=C$$

Proof

Step	Hyp	Ref	Expression
1		eleq2	$$⊢B=C\to \left(A\in B\leftrightarrow A\in C\right)$$
2	1	biimpcd	$$⊢A\in B\to \left(B=C\to A\in C\right)$$
3	2	con3dimp	$$⊢\left(A\in B\wedge \neg A\in C\right)\to \neg B=C$$