Description: Lemma for mumul . A multiple of a non-squarefree number is non-squarefree. (Contributed by Mario Carneiro, 3-Oct-2014)
Ref | Expression | ||
---|---|---|---|
Assertion | mumullem1 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | prmz | |
|
2 | 1 | adantl | |
3 | zsqcl | |
|
4 | 2 3 | syl | |
5 | nnz | |
|
6 | 5 | ad2antrr | |
7 | nnz | |
|
8 | 7 | ad2antlr | |
9 | dvdsmultr1 | |
|
10 | 4 6 8 9 | syl3anc | |
11 | 10 | reximdva | |
12 | isnsqf | |
|
13 | 12 | adantr | |
14 | nnmulcl | |
|
15 | isnsqf | |
|
16 | 14 15 | syl | |
17 | 11 13 16 | 3imtr4d | |
18 | 17 | imp | |