Description: Value of a complex number raised to the 0th power. (Contributed by Mario Carneiro, 28-May-2016)
Ref | Expression | ||
---|---|---|---|
Hypothesis | expcld.1 | ⊢ ( 𝜑 → 𝐴 ∈ ℂ ) | |
Assertion | exp0d | ⊢ ( 𝜑 → ( 𝐴 ↑ 0 ) = 1 ) |
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 ) |