Description: Inclusion in complement of complement. Part of Proposition 1 of Kalmbach p. 65. (Contributed by NM, 10-Oct-1999) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | shococss | |- ( A e. SH -> A C_ ( _|_ ` ( _|_ ` A ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | shss | |- ( A e. SH -> A C_ ~H ) |
|
| 2 | ococss | |- ( A C_ ~H -> A C_ ( _|_ ` ( _|_ ` A ) ) ) |
|
| 3 | 1 2 | syl | |- ( A e. SH -> A C_ ( _|_ ` ( _|_ ` A ) ) ) |