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	|- -. B e. C
Assertion	eqneltri	|- -. A e. C

Proof

Step	Hyp	Ref	Expression
1		eqneltri.1	|- A = B
2		eqneltri.2	|- -. B e. C
3	1	eleq1i	|- ( A e. C <-> B e. C )
4	2 3	mtbir	|- -. A e. C