Theorem replimd

Description: Construct a complex number from its real and imaginary parts. (Contributed by Mario Carneiro, 29-May-2016)

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

Proof

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