Theorem ltnsymi

Description: 'Less than' is not symmetric. (Contributed by NM, 6-May-1999)

	Ref	Expression
Hypotheses	lt.1	|- A e. RR
	lt.2	|- B e. RR
Assertion	ltnsymi	|- ( A < B -> -. B < A )

Proof

Step	Hyp	Ref	Expression
1		lt.1	|- A e. RR
2		lt.2	|- B e. RR
3		ltnsym	|- ( ( A e. RR /\ B e. RR ) -> ( A < B -> -. B < A ) )
4	1 2 3	mp2an	|- ( A < B -> -. B < A )