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) (Proof shortened by BJ, 16-Oct-2026)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | relres | |- Rel ( A |` B ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | relinxp | |- Rel ( A i^i ( B X. _V ) ) |
|
| 2 | df-res | |- ( A |` B ) = ( A i^i ( B X. _V ) ) |
|
| 3 | 2 | releqi | |- ( Rel ( A |` B ) <-> Rel ( A i^i ( B X. _V ) ) ) |
| 4 | 1 3 | mpbir | |- Rel ( A |` B ) |