Description: If an integer divides another, it divides a multiple of it. (Contributed by Paul Chapman, 17-Nov-2012)
Ref | Expression | ||
---|---|---|---|
Assertion | dvdsmultr2 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dvdsmul2 | |
|
2 | 1 | biantrud | |
3 | 2 | 3adant1 | |
4 | simp1 | |
|
5 | simp3 | |
|
6 | zmulcl | |
|
7 | 6 | 3adant1 | |
8 | dvdstr | |
|
9 | 4 5 7 8 | syl3anc | |
10 | 3 9 | sylbid | |