Theorem absidd

Description: A nonnegative number is its own absolute value. (Contributed by Mario Carneiro, 29-May-2016)

	Ref	Expression
Hypotheses	resqrcld.1	|- ( ph -> A e. RR )
	resqrcld.2	|- ( ph -> 0 <_ A )
Assertion	absidd	|- ( ph -> ( abs ` A ) = A )

Proof

Step	Hyp	Ref	Expression
1		resqrcld.1	|- ( ph -> A e. RR )
2		resqrcld.2	|- ( ph -> 0 <_ A )
3		absid	|- ( ( A e. RR /\ 0 <_ A ) -> ( abs ` A ) = A )
4	1 2 3	syl2anc	|- ( ph -> ( abs ` A ) = A )