Theorem absval2i

Description: Value of absolute value function. Definition 10.36 of Gleason p. 133. (Contributed by NM, 2-Oct-1999)

	Ref	Expression
Hypothesis	absvalsqi.1	|- A e. CC
Assertion	absval2i	|- ( abs ` A ) = ( sqrt ` ( ( ( Re ` A ) ^ 2 ) + ( ( Im ` A ) ^ 2 ) ) )

Proof

Step	Hyp	Ref	Expression
1		absvalsqi.1	|- A e. CC
2		absval2	|- ( A e. CC -> ( abs ` A ) = ( sqrt ` ( ( ( Re ` A ) ^ 2 ) + ( ( Im ` A ) ^ 2 ) ) ) )
3	1 2	ax-mp	|- ( abs ` A ) = ( sqrt ` ( ( ( Re ` A ) ^ 2 ) + ( ( Im ` A ) ^ 2 ) ) )