Theorem rpexpcld

Description: Closure law for exponentiation of positive reals. (Contributed by Mario Carneiro, 28-May-2016)

	Ref	Expression
Hypotheses	rpexpcld.1	|- ( ph -> A e. RR+ )
	rpexpcld.2	|- ( ph -> N e. ZZ )
Assertion	rpexpcld	|- ( ph -> ( A ^ N ) e. RR+ )

Proof

Step	Hyp	Ref	Expression
1		rpexpcld.1	|- ( ph -> A e. RR+ )
2		rpexpcld.2	|- ( ph -> N e. ZZ )
3		rpexpcl	|- ( ( A e. RR+ /\ N e. ZZ ) -> ( A ^ N ) e. RR+ )
4	1 2 3	syl2anc	|- ( ph -> ( A ^ N ) e. RR+ )