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 ∈ ℂ
Assertion	replimi	⊢ 𝐴 = ( ( ℜ ‘ 𝐴 ) + ( i · ( ℑ ‘ 𝐴 ) ) )

Proof

Step	Hyp	Ref	Expression
1		recl.1	⊢ 𝐴 ∈ ℂ
2		replim	⊢ ( 𝐴 ∈ ℂ → 𝐴 = ( ( ℜ ‘ 𝐴 ) + ( i · ( ℑ ‘ 𝐴 ) ) ) )
3	1 2	ax-mp	⊢ 𝐴 = ( ( ℜ ‘ 𝐴 ) + ( i · ( ℑ ‘ 𝐴 ) ) )