Theorem addcji

Description: A number plus its conjugate is twice its real part. Compare Proposition 10-3.4(h) of Gleason p. 133. (Contributed by NM, 2-Oct-1999)

	Ref	Expression
Hypothesis	recl.1	$$⊢A\in ℂ$$
Assertion	addcji	$$⊢A+\bar{A}=2\Re \left(A\right)$$

Proof

Step	Hyp	Ref	Expression
1		recl.1	$$⊢A\in ℂ$$
2		addcj	$$⊢A\in ℂ\to A+\bar{A}=2\Re \left(A\right)$$
3	1 2	ax-mp	$$⊢A+\bar{A}=2\Re \left(A\right)$$