Theorem nnsqcld

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

	Ref	Expression
Hypothesis	nnexpcld.1	|- ( ph -> A e. NN )
Assertion	nnsqcld	|- ( ph -> ( A ^ 2 ) e. NN )

Proof

Step	Hyp	Ref	Expression
1		nnexpcld.1	|- ( ph -> A e. NN )
2		nnsqcl	|- ( A e. NN -> ( A ^ 2 ) e. NN )
3	1 2	syl	|- ( ph -> ( A ^ 2 ) e. NN )