Description: Intersection preserves subclass relationship. (Contributed by Glauco Siliprandi, 17-Aug-2020)
Ref | Expression | ||
---|---|---|---|
Hypothesis | ssinss2d.1 | |- ( ph -> B C_ C ) |
|
Assertion | ssinss2d | |- ( ph -> ( A i^i B ) C_ C ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssinss2d.1 | |- ( ph -> B C_ C ) |
|
2 | incom | |- ( A i^i B ) = ( B i^i A ) |
|
3 | 1 | ssinss1d | |- ( ph -> ( B i^i A ) C_ C ) |
4 | 2 3 | eqsstrid | |- ( ph -> ( A i^i B ) C_ C ) |