Theorem nn0mulcld

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

	Ref	Expression
Hypotheses	nn0red.1	|- ( ph -> A e. NN0 )
	nn0addcld.2	|- ( ph -> B e. NN0 )
Assertion	nn0mulcld	|- ( ph -> ( A x. B ) e. NN0 )

Proof

Step	Hyp	Ref	Expression
1		nn0red.1	|- ( ph -> A e. NN0 )
2		nn0addcld.2	|- ( ph -> B e. NN0 )
3		nn0mulcl	|- ( ( A e. NN0 /\ B e. NN0 ) -> ( A x. B ) e. NN0 )
4	1 2 3	syl2anc	|- ( ph -> ( A x. B ) e. NN0 )