Theorem ltned

Description: 'Greater than' implies not equal. (Contributed by Mario Carneiro, 27-May-2016)

	Ref	Expression
Hypotheses	ltd.1	$$⊢\phi \to A\in ℝ$$
	ltned.2	$$⊢\phi \to A<B$$
Assertion	ltned	$$⊢\phi \to A\ne B$$

Proof

Step	Hyp	Ref	Expression
1		ltd.1	$$⊢\phi \to A\in ℝ$$
2		ltned.2	$$⊢\phi \to A<B$$
3	1 2	gtned	$$⊢\phi \to B\ne A$$
4	3	necomd	$$⊢\phi \to A\ne B$$