Theorem ltnri

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

	Ref	Expression
Hypothesis	lt.1	⊢ 𝐴 ∈ ℝ
Assertion	ltnri	⊢ ¬ 𝐴 < 𝐴

Proof

Step	Hyp	Ref	Expression
1		lt.1	⊢ 𝐴 ∈ ℝ
2		ltnr	⊢ ( 𝐴 ∈ ℝ → ¬ 𝐴 < 𝐴 )
3	1 2	ax-mp	⊢ ¬ 𝐴 < 𝐴