Description: A restriction is a relation. Exercise 12 of TakeutiZaring p. 25. (Contributed by NM, 2-Aug-1994) (Proof shortened by Andrew Salmon, 27-Aug-2011)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | relres | |- Rel ( A |` B ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df-res | |- ( A |` B ) = ( A i^i ( B X. _V ) ) |
|
| 2 | inss2 | |- ( A i^i ( B X. _V ) ) C_ ( B X. _V ) |
|
| 3 | 1 2 | eqsstri | |- ( A |` B ) C_ ( B X. _V ) |
| 4 | relxp | |- Rel ( B X. _V ) |
|
| 5 | relss | |- ( ( A |` B ) C_ ( B X. _V ) -> ( Rel ( B X. _V ) -> Rel ( A |` B ) ) ) |
|
| 6 | 3 4 5 | mp2 | |- Rel ( A |` B ) |