Theorem cxpgt0d

Description: A positive real raised to a real power is positive. (Contributed by SN, 6-Apr-2023)

	Ref	Expression
Hypotheses	cxpgt0d.1	|- ( ph -> A e. RR+ )
	cxpgt0d.2	|- ( ph -> N e. RR )
Assertion	cxpgt0d	|- ( ph -> 0 < ( A ^c N ) )

Proof

Step	Hyp	Ref	Expression
1		cxpgt0d.1	|- ( ph -> A e. RR+ )
2		cxpgt0d.2	|- ( ph -> N e. RR )
3	1 2	rpcxpcld	|- ( ph -> ( A ^c N ) e. RR+ )
4	3	rpgt0d	|- ( ph -> 0 < ( A ^c N ) )