Description: The naturals are closed under squaring. (Contributed by Mario Carneiro, 28-May-2016)
Ref | Expression | ||
---|---|---|---|
Hypothesis | nnexpcld.1 | ⊢ ( 𝜑 → 𝐴 ∈ ℕ ) | |
Assertion | nnsqcld | ⊢ ( 𝜑 → ( 𝐴 ↑ 2 ) ∈ ℕ ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nnexpcld.1 | ⊢ ( 𝜑 → 𝐴 ∈ ℕ ) | |
2 | nnsqcl | ⊢ ( 𝐴 ∈ ℕ → ( 𝐴 ↑ 2 ) ∈ ℕ ) | |
3 | 1 2 | syl | ⊢ ( 𝜑 → ( 𝐴 ↑ 2 ) ∈ ℕ ) |