Description: Value of the complex power function at one. (Contributed by Mario Carneiro, 30-May-2016)
Ref | Expression | ||
---|---|---|---|
Hypothesis | cxp0d.1 | ⊢ ( 𝜑 → 𝐴 ∈ ℂ ) | |
Assertion | cxp1d | ⊢ ( 𝜑 → ( 𝐴 ↑_{𝑐} 1 ) = 𝐴 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cxp0d.1 | ⊢ ( 𝜑 → 𝐴 ∈ ℂ ) | |
2 | cxp1 | ⊢ ( 𝐴 ∈ ℂ → ( 𝐴 ↑_{𝑐} 1 ) = 𝐴 ) | |
3 | 1 2 | syl | ⊢ ( 𝜑 → ( 𝐴 ↑_{𝑐} 1 ) = 𝐴 ) |