Theorem absred

Description: Absolute value of a real number. (Contributed by Mario Carneiro, 29-May-2016)

	Ref	Expression
Hypothesis	resqrcld.1	|- ( ph -> A e. RR )
Assertion	absred	|- ( ph -> ( abs ` A ) = ( sqrt ` ( A ^ 2 ) ) )

Proof

Step	Hyp	Ref	Expression
1		resqrcld.1	|- ( ph -> A e. RR )
2		absre	|- ( A e. RR -> ( abs ` A ) = ( sqrt ` ( A ^ 2 ) ) )
3	1 2	syl	|- ( ph -> ( abs ` A ) = ( sqrt ` ( A ^ 2 ) ) )