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 ) ) |