Theorem nnmulcli

Description: Closure of multiplication of positive integers. (Contributed by Mario Carneiro, 18-Feb-2014)

	Ref	Expression
Hypotheses	nnmulcli.1	|- A e. NN
	nnmulcli.2	|- B e. NN
Assertion	nnmulcli	|- ( A x. B ) e. NN

Proof

Step	Hyp	Ref	Expression
1		nnmulcli.1	|- A e. NN
2		nnmulcli.2	|- B e. NN
3		nnmulcl	|- ( ( A e. NN /\ B e. NN ) -> ( A x. B ) e. NN )
4	1 2 3	mp2an	|- ( A x. B ) e. NN