Description: A positive integer decreased by 1 is greater than or equal to 0. (Contributed by AV, 30-Oct-2018)
Ref | Expression | ||
---|---|---|---|
Assertion | nnm1ge0 | |- ( N e. NN -> 0 <_ ( N - 1 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nngt0 | |- ( N e. NN -> 0 < N ) |
|
2 | 0z | |- 0 e. ZZ |
|
3 | nnz | |- ( N e. NN -> N e. ZZ ) |
|
4 | zltlem1 | |- ( ( 0 e. ZZ /\ N e. ZZ ) -> ( 0 < N <-> 0 <_ ( N - 1 ) ) ) |
|
5 | 2 3 4 | sylancr | |- ( N e. NN -> ( 0 < N <-> 0 <_ ( N - 1 ) ) ) |
6 | 1 5 | mpbid | |- ( N e. NN -> 0 <_ ( N - 1 ) ) |