Description: Difference law for Cartesian products. (Contributed by Thierry Arnoux, 24-Jul-2023)
Ref | Expression | ||
---|---|---|---|
Assertion | difxp1ss | |- ( ( A \ C ) X. B ) C_ ( A X. B ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | difxp1 | |- ( ( A \ C ) X. B ) = ( ( A X. B ) \ ( C X. B ) ) |
|
2 | difss | |- ( ( A X. B ) \ ( C X. B ) ) C_ ( A X. B ) |
|
3 | 1 2 | eqsstri | |- ( ( A \ C ) X. B ) C_ ( A X. B ) |