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