Description: An integer divides another iff it divides their sum. (Contributed by Paul Chapman, 31-Mar-2011) (Revised by Mario Carneiro, 13-Jul-2014)
Ref | Expression | ||
---|---|---|---|
Assertion | dvdsadd | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl | |
|
2 | zaddcl | |
|
3 | simpr | |
|
4 | iddvds | |
|
5 | 4 | adantr | |
6 | zcn | |
|
7 | zcn | |
|
8 | pncan | |
|
9 | 6 7 8 | syl2an | |
10 | 5 9 | breqtrrd | |
11 | dvdssub2 | |
|
12 | 1 2 3 10 11 | syl31anc | |
13 | 12 | bicomd | |