Description: Second Peano postulate for an upper set of integers. (Contributed by Mario Carneiro, 26-Dec-2013)
Ref | Expression | ||
---|---|---|---|
Hypothesis | peano2uzs.1 | |- Z = ( ZZ>= ` M ) |
|
Assertion | peano2uzs | |- ( N e. Z -> ( N + 1 ) e. Z ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | peano2uzs.1 | |- Z = ( ZZ>= ` M ) |
|
2 | peano2uz | |- ( N e. ( ZZ>= ` M ) -> ( N + 1 ) e. ( ZZ>= ` M ) ) |
|
3 | 2 1 | eleqtrrdi | |- ( N e. ( ZZ>= ` M ) -> ( N + 1 ) e. Z ) |
4 | 3 1 | eleq2s | |- ( N e. Z -> ( N + 1 ) e. Z ) |