Theorem eqneltri

Description: If a class is not an element of another class, an equal class is also not an element. (Contributed by Glauco Siliprandi, 3-Jan-2021)

	Ref	Expression
Hypotheses	eqneltri.1	$$⊢A=B$$
	eqneltri.2	$$⊢\neg B\in C$$
Assertion	eqneltri	$$⊢\neg A\in C$$

Proof

Step	Hyp	Ref	Expression
1		eqneltri.1	$$⊢A=B$$
2		eqneltri.2	$$⊢\neg B\in C$$
3	1	eleq1i	$$⊢A\in C\leftrightarrow B\in C$$
4	2 3	mtbir	$$⊢\neg A\in C$$