Description: The sum of a positive integer and a nonnegative integer less than the positive integer is equal to the nonnegative integer modulo the positive integer. (Contributed by AV, 19-Mar-2021)
Ref | Expression | ||
---|---|---|---|
Assertion | addmodidr | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nn0cn | |
|
2 | nncn | |
|
3 | addcom | |
|
4 | 1 2 3 | syl2an | |
5 | 4 | 3adant3 | |
6 | 5 | oveq1d | |
7 | addmodid | |
|
8 | 6 7 | eqtrd | |