Description: Postcomposition is subdistributive over intersection. Compare with coundi . See coindi for equality when postcomposing with an injective class. (Contributed by BJ, 8-Nov-2026)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | coindiss | |- ( A o. ( B i^i C ) ) C_ ( ( A o. B ) i^i ( A o. C ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | inss1 | |- ( B i^i C ) C_ B |
|
| 2 | coss2 | |- ( ( B i^i C ) C_ B -> ( A o. ( B i^i C ) ) C_ ( A o. B ) ) |
|
| 3 | 1 2 | ax-mp | |- ( A o. ( B i^i C ) ) C_ ( A o. B ) |
| 4 | inss2 | |- ( B i^i C ) C_ C |
|
| 5 | coss2 | |- ( ( B i^i C ) C_ C -> ( A o. ( B i^i C ) ) C_ ( A o. C ) ) |
|
| 6 | 4 5 | ax-mp | |- ( A o. ( B i^i C ) ) C_ ( A o. C ) |
| 7 | 3 6 | ssini | |- ( A o. ( B i^i C ) ) C_ ( ( A o. B ) i^i ( A o. C ) ) |