Metamath Proof Explorer


Theorem dvdsmultr1

Description: If an integer divides another, it divides a multiple of it. (Contributed by Paul Chapman, 17-Nov-2012)

Ref Expression
Assertion dvdsmultr1 KMNKMK M N

Proof

Step Hyp Ref Expression
1 dvdsmul1 MNM M N
2 1 3adant1 KMNM M N
3 zmulcl MN M N
4 3 3adant1 KMN M N
5 dvdstr KM M NKMM M NK M N
6 4 5 syld3an3 KMNKMM M NK M N
7 2 6 mpan2d KMNKMK M N