Description: Difference law for Cartesian products. (Contributed by Thierry Arnoux, 24-Jul-2023)
Ref | Expression | ||
---|---|---|---|
Assertion | difxp2ss | |- ( A X. ( B \ C ) ) C_ ( A X. B ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | difxp2 | |- ( A X. ( B \ C ) ) = ( ( A X. B ) \ ( A X. C ) ) |
|
2 | difss | |- ( ( A X. B ) \ ( A X. C ) ) C_ ( A X. B ) |
|
3 | 1 2 | eqsstri | |- ( A X. ( B \ C ) ) C_ ( A X. B ) |