Description: An element of a power class is a subclass. Deduction form of elpwi . (Contributed by David Moews, 1-May-2017)
Ref | Expression | ||
---|---|---|---|
Hypothesis | elpwid.1 | |- ( ph -> A e. ~P B ) |
|
Assertion | elpwid | |- ( ph -> A C_ B ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elpwid.1 | |- ( ph -> A e. ~P B ) |
|
2 | elpwi | |- ( A e. ~P B -> A C_ B ) |
|
3 | 1 2 | syl | |- ( ph -> A C_ B ) |