Theorem ltneii

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

	Ref	Expression
Hypotheses	lt.1	⊢ 𝐴 ∈ ℝ
	ltneii.2	⊢ 𝐴 < 𝐵
Assertion	ltneii	⊢ 𝐴 ≠ 𝐵

Proof

Step	Hyp	Ref	Expression
1		lt.1	⊢ 𝐴 ∈ ℝ
2		ltneii.2	⊢ 𝐴 < 𝐵
3	1 2	gtneii	⊢ 𝐵 ≠ 𝐴
4	3	necomi	⊢ 𝐴 ≠ 𝐵