Theorem expcld

Description: Closure law for nonnegative integer exponentiation. (Contributed by Mario Carneiro, 28-May-2016)

	Ref	Expression
Hypotheses	expcld.1	|- ( ph -> A e. CC )
	expcld.2	|- ( ph -> N e. NN0 )
Assertion	expcld	|- ( ph -> ( A ^ N ) e. CC )

Proof

Step	Hyp	Ref	Expression
1		expcld.1	|- ( ph -> A e. CC )
2		expcld.2	|- ( ph -> N e. NN0 )
3		expcl	|- ( ( A e. CC /\ N e. NN0 ) -> ( A ^ N ) e. CC )
4	1 2 3	syl2anc	|- ( ph -> ( A ^ N ) e. CC )