Description: The exponentiation of a relation is a relation. (Contributed by RP, 23-May-2020)
Ref | Expression | ||
---|---|---|---|
Assertion | relexprel | |- ( ( N e. NN0 /\ R e. V /\ Rel R ) -> Rel ( R ^r N ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-1 | |- ( Rel R -> ( N = 1 -> Rel R ) ) |
|
2 | relexprelg | |- ( ( N e. NN0 /\ R e. V /\ ( N = 1 -> Rel R ) ) -> Rel ( R ^r N ) ) |
|
3 | 1 2 | syl3an3 | |- ( ( N e. NN0 /\ R e. V /\ Rel R ) -> Rel ( R ^r N ) ) |