Theorem absori

Description: The absolute value of a real number is either that number or its negative. (Contributed by NM, 30-Sep-1999)

	Ref	Expression
Hypothesis	sqrtthi.1	|- A e. RR
Assertion	absori	|- ( ( abs ` A ) = A \/ ( abs ` A ) = -u A )

Proof

Step	Hyp	Ref	Expression
1		sqrtthi.1	|- A e. RR
2		absor	|- ( A e. RR -> ( ( abs ` A ) = A \/ ( abs ` A ) = -u A ) )
3	1 2	ax-mp	|- ( ( abs ` A ) = A \/ ( abs ` A ) = -u A )