Theorem replimi

Description: Construct a complex number from its real and imaginary parts. (Contributed by NM, 1-Oct-1999)

	Ref	Expression
Hypothesis	recl.1	$$⊢A\in ℂ$$
Assertion	replimi	$$⊢A=\Re \left(A\right)+\mathrm{i}\Im \left(A\right)$$

Proof

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