Theorem abscjd

Description: The absolute value of a number and its conjugate are the same. Proposition 10-3.7(b) of Gleason p. 133. (Contributed by Mario Carneiro, 29-May-2016)

	Ref	Expression
Hypothesis	abscld.1	$$⊢\phi \to A\in ℂ$$
Assertion	abscjd	$$⊢\phi \to \left|\bar{A}\right|=\left|A\right|$$

Proof

Step	Hyp	Ref	Expression
1		abscld.1	$$⊢\phi \to A\in ℂ$$
2		abscj	$$⊢A\in ℂ\to \left|\bar{A}\right|=\left|A\right|$$
3	1 2	syl	$$⊢\phi \to \left|\bar{A}\right|=\left|A\right|$$