Theorem ltnri

Description: 'Less than' is irreflexive. (Contributed by NM, 18-Aug-1999)

	Ref	Expression
Hypothesis	lt.1	$$⊢A\in ℝ$$
Assertion	ltnri	$$⊢\neg A<A$$

Proof

Step	Hyp	Ref	Expression
1		lt.1	$$⊢A\in ℝ$$
2		ltnr	$$⊢A\in ℝ\to \neg A<A$$
3	1 2	ax-mp	$$⊢\neg A<A$$