Theorem absord

Description: The absolute value of a real number is either that number or its negative. (Contributed by Mario Carneiro, 29-May-2016)

	Ref	Expression
Hypothesis	resqrcld.1	|- ( ph -> A e. RR )
Assertion	absord	|- ( ph -> ( ( abs ` A ) = A \/ ( abs ` A ) = -u A ) )

Proof

Step	Hyp	Ref	Expression
1		resqrcld.1	|- ( ph -> A e. RR )
2		absor	|- ( A e. RR -> ( ( abs ` A ) = A \/ ( abs ` A ) = -u A ) )
3	1 2	syl	|- ( ph -> ( ( abs ` A ) = A \/ ( abs ` A ) = -u A ) )