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Metamath Proof Explorer

Theorem cxp0d

Description: Value of the complex power function when the second argument is zero. (Contributed by Mario Carneiro, 30-May-2016)

Ref Expression
Hypothesis cxp0d.1 ⊢ ( 𝜑 → 𝐴 ∈ ℂ )
Assertion cxp0d ( 𝜑 → ( 𝐴 ↑𝑐 0 ) = 1 )

Proof

Step Hyp Ref Expression
1 cxp0d.1 ⊢ ( 𝜑 → 𝐴 ∈ ℂ )
2 cxp0 ⊢ ( 𝐴 ∈ ℂ → ( 𝐴 ↑𝑐 0 ) = 1 )
3 1 2 syl ⊢ ( 𝜑 → ( 𝐴 ↑𝑐 0 ) = 1 )