Metamath Proof Explorer

Theorem exp0d

Description: Value of a complex number raised to the 0th power. (Contributed by Mario Carneiro, 28-May-2016)

Ref Expression
Hypothesis expcld.1 
|- ( ph -> A e. CC )
Assertion exp0d 
|- ( ph -> ( A ^ 0 ) = 1 )

Proof

Step Hyp Ref Expression
1 expcld.1 
 |-  ( ph -> A e. CC )
2 exp0 
 |-  ( A e. CC -> ( A ^ 0 ) = 1 )
3 1 2 syl 
 |-  ( ph -> ( A ^ 0 ) = 1 )