Theorem ltnr

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

	Ref	Expression
Assertion	ltnr	⊢ ( 𝐴 ∈ ℝ → ¬ 𝐴 < 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		ltso	⊢ < Or ℝ
2		sonr	⊢ ( ( < Or ℝ ∧ 𝐴 ∈ ℝ ) → ¬ 𝐴 < 𝐴 )
3	1 2	mpan	⊢ ( 𝐴 ∈ ℝ → ¬ 𝐴 < 𝐴 )