Description: The powerclass preserves inclusion (deduction form). (Contributed by BJ, 13-Apr-2024)
Ref | Expression | ||
---|---|---|---|
Hypothesis | sspwd.1 | |- ( ph -> A C_ B ) |
|
Assertion | sspwd | |- ( ph -> ~P A C_ ~P B ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sspwd.1 | |- ( ph -> A C_ B ) |
|
2 | sspw | |- ( A C_ B -> ~P A C_ ~P B ) |
|
3 | 1 2 | syl | |- ( ph -> ~P A C_ ~P B ) |