Theorem ltnr

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

	Ref	Expression
Assertion	ltnr	|- ( A e. RR -> -. A < A )

Proof

Step	Hyp	Ref	Expression
1		ltso	|- < Or RR
2		sonr	|- ( ( < Or RR /\ A e. RR ) -> -. A < A )
3	1 2	mpan	|- ( A e. RR -> -. A < A )