Description: The Legendre symbol is an integer. (Contributed by Mario Carneiro, 4-Feb-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | lgscl | |- ( ( A e. ZZ /\ N e. ZZ ) -> ( A /L N ) e. ZZ ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssrab2 | |- { x e. ZZ | ( abs ` x ) <_ 1 } C_ ZZ |
|
2 | eqid | |- { x e. ZZ | ( abs ` x ) <_ 1 } = { x e. ZZ | ( abs ` x ) <_ 1 } |
|
3 | 2 | lgscl2 | |- ( ( A e. ZZ /\ N e. ZZ ) -> ( A /L N ) e. { x e. ZZ | ( abs ` x ) <_ 1 } ) |
4 | 1 3 | sselid | |- ( ( A e. ZZ /\ N e. ZZ ) -> ( A /L N ) e. ZZ ) |