Theorem pccld

Description: Closure of the prime power function. (Contributed by Mario Carneiro, 29-May-2016)

	Ref	Expression
Hypotheses	pccld.1	|- ( ph -> P e. Prime )
	pccld.2	|- ( ph -> N e. NN )
Assertion	pccld	|- ( ph -> ( P pCnt N ) e. NN0 )

Proof

Step	Hyp	Ref	Expression
1		pccld.1	|- ( ph -> P e. Prime )
2		pccld.2	|- ( ph -> N e. NN )
3		pccl	|- ( ( P e. Prime /\ N e. NN ) -> ( P pCnt N ) e. NN0 )
4	1 2 3	syl2anc	|- ( ph -> ( P pCnt N ) e. NN0 )