Theorem eff1o2

Description: The exponential function restricted to its principal domain maps one-to-one onto the nonzero complex numbers. (Contributed by Paul Chapman, 21-Apr-2008) (Revised by Mario Carneiro, 13-May-2014)

	Ref	Expression
Assertion	eff1o2	⊢ ( exp ↾ ran log ) : ran log –1-1-onto→ ( ℂ ∖ { 0 } )

Proof

Step	Hyp	Ref	Expression
1		logrn	⊢ ran log = ( ◡ ℑ “ ( - π (,] π ) )
2	1	eff1o	⊢ ( exp ↾ ran log ) : ran log –1-1-onto→ ( ℂ ∖ { 0 } )