Theorem recji

Description: Real part of a complex conjugate. (Contributed by NM, 2-Oct-1999)

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

Proof

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