Theorem efiargd

Description: The exponential of the "arg" function Im o. log , deduction version. (Contributed by Thierry Arnoux, 5-Nov-2025)

	Ref	Expression
Hypotheses	efiargd.1	|- ( ph -> A e. CC )
	efiargd.2	|- ( ph -> A =/= 0 )
Assertion	efiargd	|- ( ph -> ( exp ` ( _i x. ( Im ` ( log ` A ) ) ) ) = ( A / ( abs ` A ) ) )

Proof

Step	Hyp	Ref	Expression
1		efiargd.1	|- ( ph -> A e. CC )
2		efiargd.2	|- ( ph -> A =/= 0 )
3		efiarg	|- ( ( A e. CC /\ A =/= 0 ) -> ( exp ` ( _i x. ( Im ` ( log ` A ) ) ) ) = ( A / ( abs ` A ) ) )
4	1 2 3	syl2anc	|- ( ph -> ( exp ` ( _i x. ( Im ` ( log ` A ) ) ) ) = ( A / ( abs ` A ) ) )