Description: Closure of join in SH . (Contributed by NM, 2-Nov-1999) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Assertion | shjcl | |- ( ( A e. SH /\ B e. SH ) -> ( A vH B ) e. CH ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | shss | |- ( A e. SH -> A C_ ~H ) |
|
2 | shss | |- ( B e. SH -> B C_ ~H ) |
|
3 | sshjcl | |- ( ( A C_ ~H /\ B C_ ~H ) -> ( A vH B ) e. CH ) |
|
4 | 1 2 3 | syl2an | |- ( ( A e. SH /\ B e. SH ) -> ( A vH B ) e. CH ) |