Theorem nnsqcld

Description: The naturals are closed under squaring. (Contributed by Mario Carneiro, 28-May-2016)

	Ref	Expression
Hypothesis	nnexpcld.1	$$⊢\phi \to A\in \mathbb{N}$$
Assertion	nnsqcld	$$⊢\phi \to A^2\in \mathbb{N}$$

Proof

Step	Hyp	Ref	Expression
1		nnexpcld.1	$$⊢\phi \to A\in \mathbb{N}$$
2		nnsqcl	$$⊢A\in \mathbb{N}\to A^2\in \mathbb{N}$$
3	1 2	syl	$$⊢\phi \to A^2\in \mathbb{N}$$