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	|- ( ph -> A e. CC )
Assertion	replimd	|- ( ph -> A = ( ( Re ` A ) + ( _i x. ( Im ` A ) ) ) )

Proof

Step	Hyp	Ref	Expression
1		recld.1	|- ( ph -> A e. CC )
2		replim	|- ( A e. CC -> A = ( ( Re ` A ) + ( _i x. ( Im ` A ) ) ) )
3	1 2	syl	|- ( ph -> A = ( ( Re ` A ) + ( _i x. ( Im ` A ) ) ) )