Theorem nn0mulcli

Description: Closure of multiplication of nonnegative integers, inference form. (Contributed by Raph Levien, 10-Dec-2002)

	Ref	Expression
Hypotheses	nn0addcli.1	|- M e. NN0
	nn0addcli.2	|- N e. NN0
Assertion	nn0mulcli	|- ( M x. N ) e. NN0

Proof

Step	Hyp	Ref	Expression
1		nn0addcli.1	|- M e. NN0
2		nn0addcli.2	|- N e. NN0
3		nn0mulcl	|- ( ( M e. NN0 /\ N e. NN0 ) -> ( M x. N ) e. NN0 )
4	1 2 3	mp2an	|- ( M x. N ) e. NN0