This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

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