Theorem nnmcli

Description: _om is closed under multiplication. Inference form of nnmcl . (Contributed by Scott Fenton, 20-Apr-2012)

	Ref	Expression
Hypotheses	nncli.1	|- A e. _om
	nncli.2	|- B e. _om
Assertion	nnmcli	|- ( A .o B ) e. _om

Proof

Step	Hyp	Ref	Expression
1		nncli.1	|- A e. _om
2		nncli.2	|- B e. _om
3		nnmcl	|- ( ( A e. _om /\ B e. _om ) -> ( A .o B ) e. _om )
4	1 2 3	mp2an	|- ( A .o B ) e. _om