Theorem ltnrd

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

	Ref	Expression
Hypothesis	ltd.1	$$⊢\phi \to A\in ℝ$$
Assertion	ltnrd	$$⊢\phi \to \neg A<A$$

Proof

Step	Hyp	Ref	Expression
1		ltd.1	$$⊢\phi \to A\in ℝ$$
2		ltnr	$$⊢A\in ℝ\to \neg A<A$$
3	1 2	syl	$$⊢\phi \to \neg A<A$$