Description: Positive integer ordering relation. (Contributed by NM, 21-Jun-2005)
Ref | Expression | ||
---|---|---|---|
Assertion | nnltlem1 | |- ( ( M e. NN /\ N e. NN ) -> ( M < N <-> M <_ ( N - 1 ) ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nnz | |- ( M e. NN -> M e. ZZ ) |
|
2 | nnz | |- ( N e. NN -> N e. ZZ ) |
|
3 | zltlem1 | |- ( ( M e. ZZ /\ N e. ZZ ) -> ( M < N <-> M <_ ( N - 1 ) ) ) |
|
4 | 1 2 3 | syl2an | |- ( ( M e. NN /\ N e. NN ) -> ( M < N <-> M <_ ( N - 1 ) ) ) |