Metamath Proof Explorer


Theorem exp0d

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

Ref Expression
Hypothesis expcld.1 ⊢ φ → A ∈ ℂ
Assertion exp0d ⊢ φ → A 0 = 1

Proof

Step Hyp Ref Expression
1 expcld.1 ⊢ φ → A ∈ ℂ
2 exp0 ⊢ A ∈ ℂ → A 0 = 1
3 1 2 syl ⊢ φ → A 0 = 1