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Metamath Proof Explorer

Theorem ltnr

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

		Ref	Expression
	Assertion	ltnr	$⊢ A \in ℝ \to \neg A < A$

Step	Hyp	Ref	Expression
1		ltso	$⊢ < Or ℝ$
2		sonr	$⊢ (< Or ℝ \land A \in ℝ) \to \neg A < A$
3	1 2	mpan	$⊢ A \in ℝ \to \neg A < A$