Theorem gtneii

Description: 'Less than' implies not equal. (Contributed by Mario Carneiro, 30-Sep-2013)

	Ref	Expression
Hypotheses	lt.1	|- A e. RR
	ltneii.2	|- A < B
Assertion	gtneii	|- B =/= A

Proof

Step	Hyp	Ref	Expression
1		lt.1	|- A e. RR
2		ltneii.2	|- A < B
3		ltne	|- ( ( A e. RR /\ A < B ) -> B =/= A )
4	1 2 3	mp2an	|- B =/= A