Description: Nonnegative integer ordering relation. (Contributed by Raph Levien, 10-Apr-2004)
Ref | Expression | ||
---|---|---|---|
Assertion | nn0leltp1 | |- ( ( M e. NN0 /\ N e. NN0 ) -> ( M <_ N <-> M < ( N + 1 ) ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nn0z | |- ( M e. NN0 -> M e. ZZ ) |
|
2 | nn0z | |- ( N e. NN0 -> N e. ZZ ) |
|
3 | zleltp1 | |- ( ( M e. ZZ /\ N e. ZZ ) -> ( M <_ N <-> M < ( N + 1 ) ) ) |
|
4 | 1 2 3 | syl2an | |- ( ( M e. NN0 /\ N e. NN0 ) -> ( M <_ N <-> M < ( N + 1 ) ) ) |