Theorem absvalsq2i

Description: Square of value of absolute value function. (Contributed by NM, 2-Oct-1999)

	Ref	Expression
Hypothesis	absvalsqi.1	|- A e. CC
Assertion	absvalsq2i	|- ( ( abs ` A ) ^ 2 ) = ( ( ( Re ` A ) ^ 2 ) + ( ( Im ` A ) ^ 2 ) )

Proof

Step	Hyp	Ref	Expression
1		absvalsqi.1	|- A e. CC
2		absvalsq2	|- ( A e. CC -> ( ( abs ` A ) ^ 2 ) = ( ( ( Re ` A ) ^ 2 ) + ( ( Im ` A ) ^ 2 ) ) )
3	1 2	ax-mp	|- ( ( abs ` A ) ^ 2 ) = ( ( ( Re ` A ) ^ 2 ) + ( ( Im ` A ) ^ 2 ) )