Theorem reexpcld

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

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

Proof

Step	Hyp	Ref	Expression
1		reexpcld.1	|- ( ph -> A e. RR )
2		reexpcld.2	|- ( ph -> N e. NN0 )
3		reexpcl	|- ( ( A e. RR /\ N e. NN0 ) -> ( A ^ N ) e. RR )
4	1 2 3	syl2anc	|- ( ph -> ( A ^ N ) e. RR )