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	$$⊢A\in ℂ$$
Assertion	absval2i	$$⊢\left|A\right|=\sqrt{{\Re \left(A\right)}^2+{\Im \left(A\right)}^2}$$

Proof

Step	Hyp	Ref	Expression
1		absvalsqi.1	$$⊢A\in ℂ$$
2		absval2	$$⊢A\in ℂ\to \left|A\right|=\sqrt{{\Re \left(A\right)}^2+{\Im \left(A\right)}^2}$$
3	1 2	ax-mp	$$⊢\left|A\right|=\sqrt{{\Re \left(A\right)}^2+{\Im \left(A\right)}^2}$$