Theorem remimd

Description: Value of the conjugate of a complex number. The value is the real part minus _i times the imaginary part. Definition 10-3.2 of Gleason p. 132. (Contributed by Mario Carneiro, 29-May-2016)

	Ref	Expression
Hypothesis	recld.1	$$⊢\phi \to A\in ℂ$$
Assertion	remimd	$$⊢\phi \to \bar{A}=\Re \left(A\right)-\mathrm{i}\Im \left(A\right)$$

Proof

Step	Hyp	Ref	Expression
1		recld.1	$$⊢\phi \to A\in ℂ$$
2		remim	$$⊢A\in ℂ\to \bar{A}=\Re \left(A\right)-\mathrm{i}\Im \left(A\right)$$
3	1 2	syl	$$⊢\phi \to \bar{A}=\Re \left(A\right)-\mathrm{i}\Im \left(A\right)$$