Description: Intersection preserves subclass relationship. (Contributed by Glauco Siliprandi, 17-Aug-2020)
Ref | Expression | ||
---|---|---|---|
Hypothesis | ssinss1d.1 | |- ( ph -> A C_ C ) |
|
Assertion | ssinss1d | |- ( ph -> ( A i^i B ) C_ C ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssinss1d.1 | |- ( ph -> A C_ C ) |
|
2 | ssinss1 | |- ( A C_ C -> ( A i^i B ) C_ C ) |
|
3 | 1 2 | syl | |- ( ph -> ( A i^i B ) C_ C ) |