Metamath Proof Explorer


Theorem sqfpc

Description: The prime count of a squarefree number is at most 1. (Contributed by Mario Carneiro, 1-Jul-2015)

Ref Expression
Assertion sqfpc A μ A 0 P P pCnt A 1

Proof

Step Hyp Ref Expression
1 issqf A μ A 0 p p pCnt A 1
2 1 biimpa A μ A 0 p p pCnt A 1
3 oveq1 p = P p pCnt A = P pCnt A
4 3 breq1d p = P p pCnt A 1 P pCnt A 1
5 4 rspccv p p pCnt A 1 P P pCnt A 1
6 2 5 syl A μ A 0 P P pCnt A 1
7 6 3impia A μ A 0 P P pCnt A 1