Theorem ltnei

Description: 'Less than' implies not equal. (Contributed by NM, 28-Jul-1999)

	Ref	Expression
Hypotheses	lt.1	$$⊢A\in ℝ$$
	lt.2	$$⊢B\in ℝ$$
Assertion	ltnei	$$⊢A<B\to B\ne A$$

Proof

Step	Hyp	Ref	Expression
1		lt.1	$$⊢A\in ℝ$$
2		lt.2	$$⊢B\in ℝ$$
3		ltne	$$⊢\left(A\in ℝ\wedge A<B\right)\to B\ne A$$
4	1 3	mpan	$$⊢A<B\to B\ne A$$