Theorem addcjd

Description: A number plus its conjugate is twice its real part. Compare Proposition 10-3.4(h) of Gleason p. 133. (Contributed by Mario Carneiro, 29-May-2016)

	Ref	Expression
Hypothesis	recld.1	$$⊢\phi \to A\in ℂ$$
Assertion	addcjd	$$⊢\phi \to A+\bar{A}=2\Re \left(A\right)$$

Proof

Step	Hyp	Ref	Expression
1		recld.1	$$⊢\phi \to A\in ℂ$$
2		addcj	$$⊢A\in ℂ\to A+\bar{A}=2\Re \left(A\right)$$
3	1 2	syl	$$⊢\phi \to A+\bar{A}=2\Re \left(A\right)$$