Theorem nnsqcld

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 )

Proof

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 )