Theorem absnidi

Description: A negative number is the negative of its own absolute value. (Contributed by NM, 2-Aug-1999)

	Ref	Expression
Hypothesis	sqrtthi.1	|- A e. RR
Assertion	absnidi	|- ( A <_ 0 -> ( abs ` A ) = -u A )

Proof

Step	Hyp	Ref	Expression
1		sqrtthi.1	|- A e. RR
2		absnid	|- ( ( A e. RR /\ A <_ 0 ) -> ( abs ` A ) = -u A )
3	1 2	mpan	|- ( A <_ 0 -> ( abs ` A ) = -u A )