Description: If an integer divides a difference, then it divides one term iff it divides the other. (Contributed by Mario Carneiro, 13-Jul-2014)
Ref | Expression | ||
---|---|---|---|
Assertion | dvdssub2 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | zsubcl | |
|
2 | 1 | 3adant1 | |
3 | dvds2sub | |
|
4 | 2 3 | syld3an3 | |
5 | 4 | ancomsd | |
6 | 5 | imp | |
7 | zcn | |
|
8 | zcn | |
|
9 | nncan | |
|
10 | 7 8 9 | syl2an | |
11 | 10 | 3adant1 | |
12 | 11 | adantr | |
13 | 6 12 | breqtrd | |
14 | 13 | expr | |
15 | dvds2add | |
|
16 | 2 15 | syld3an2 | |
17 | 16 | imp | |
18 | npcan | |
|
19 | 7 8 18 | syl2an | |
20 | 19 | 3adant1 | |
21 | 20 | adantr | |
22 | 17 21 | breqtrd | |
23 | 22 | expr | |
24 | 14 23 | impbid | |