Description: Condition for the identity restriction to be equal to the identity intersection with a Cartesian product. (Contributed by Peter Mazsa, 19-Jul-2018)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | idreseqidinxp | |- ( A C_ B -> ( _I i^i ( A X. B ) ) = ( _I |` A ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | inxpssres | |- ( _I i^i ( A X. B ) ) C_ ( _I |` A ) |
|
| 2 | 1 | a1i | |- ( A C_ B -> ( _I i^i ( A X. B ) ) C_ ( _I |` A ) ) |
| 3 | idresssidinxp | |- ( A C_ B -> ( _I |` A ) C_ ( _I i^i ( A X. B ) ) ) |
|
| 4 | 2 3 | eqssd | |- ( A C_ B -> ( _I i^i ( A X. B ) ) = ( _I |` A ) ) |