Theorem nnmulcld

Description: Closure of multiplication of positive integers. (Contributed by Mario Carneiro, 27-May-2016)

	Ref	Expression
Hypotheses	nnge1d.1	|- ( ph -> A e. NN )
	nnmulcld.2	|- ( ph -> B e. NN )
Assertion	nnmulcld	|- ( ph -> ( A x. B ) e. NN )

Proof

Step	Hyp	Ref	Expression
1		nnge1d.1	|- ( ph -> A e. NN )
2		nnmulcld.2	|- ( ph -> B e. NN )
3		nnmulcl	|- ( ( A e. NN /\ B e. NN ) -> ( A x. B ) e. NN )
4	1 2 3	syl2anc	|- ( ph -> ( A x. B ) e. NN )