Theorem ltneii

Description: 'Greater than' implies not equal. (Contributed by Mario Carneiro, 16-Sep-2015)

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

Proof

Step	Hyp	Ref	Expression
1		lt.1	|- A e. RR
2		ltneii.2	|- A < B
3	1 2	gtneii	|- B =/= A
4	3	necomi	|- A =/= B