Theorem ltnrd

Description: 'Less than' is irreflexive. (Contributed by Mario Carneiro, 27-May-2016)

	Ref	Expression
Hypothesis	ltd.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
Assertion	ltnrd	⊢ ( 𝜑 → ¬ 𝐴 < 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		ltd.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
2		ltnr	⊢ ( 𝐴 ∈ ℝ → ¬ 𝐴 < 𝐴 )
3	1 2	syl	⊢ ( 𝜑 → ¬ 𝐴 < 𝐴 )