Description: Value of zero raised to a positive integer power. (Contributed by Mario Carneiro, 28-May-2016)
Ref | Expression | ||
---|---|---|---|
Hypothesis | 0exp.1 | ⊢ ( 𝜑 → 𝑁 ∈ ℕ ) | |
Assertion | 0expd | ⊢ ( 𝜑 → ( 0 ↑ 𝑁 ) = 0 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0exp.1 | ⊢ ( 𝜑 → 𝑁 ∈ ℕ ) | |
2 | 0exp | ⊢ ( 𝑁 ∈ ℕ → ( 0 ↑ 𝑁 ) = 0 ) | |
3 | 1 2 | syl | ⊢ ( 𝜑 → ( 0 ↑ 𝑁 ) = 0 ) |