This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem nelaneqOLD

Description: Obsolete version of nelaneq as of 22-Apr-2026. (Proposed by BJ, 18-Jun-2022.) (Contributed by AV, 18-Jun-2022) (Proof shortened by TM, 31-Dec-2025) (Proof modification is discouraged.) (New usage is discouraged.)

		Ref	Expression
	Assertion	nelaneqOLD	\|- -. ( A e. B /\ A = B )

Proof

Step	Hyp	Ref	Expression
1		elirr	\|- -. A e. A
2		eleq2	\|- ( A = B -> ( A e. A <-> A e. B ) )
3	1 2	mtbii	\|- ( A = B -> -. A e. B )
4	3	con2i	\|- ( A e. B -> -. A = B )
5		imnan	\|- ( ( A e. B -> -. A = B ) <-> -. ( A e. B /\ A = B ) )
6	4 5	mpbi	\|- -. ( A e. B /\ A = B )