Theorem nn0expcli

Description: Closure of exponentiation of nonnegative integers. (Contributed by Mario Carneiro, 17-Apr-2015)

	Ref	Expression
Hypotheses	nn0expcli.1	|- A e. NN0
	nn0expcli.2	|- N e. NN0
Assertion	nn0expcli	|- ( A ^ N ) e. NN0

Proof

Step	Hyp	Ref	Expression
1		nn0expcli.1	|- A e. NN0
2		nn0expcli.2	|- N e. NN0
3		nn0expcl	|- ( ( A e. NN0 /\ N e. NN0 ) -> ( A ^ N ) e. NN0 )
4	1 2 3	mp2an	|- ( A ^ N ) e. NN0