Description: Subspace sum is an upper bound of its arguments. (Contributed by NM, 17-Dec-2004) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Assertion | shsub2 | |- ( ( A e. SH /\ B e. SH ) -> A C_ ( B +H A ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | shsub1 | |- ( ( A e. SH /\ B e. SH ) -> A C_ ( A +H B ) ) |
|
2 | shscom | |- ( ( A e. SH /\ B e. SH ) -> ( A +H B ) = ( B +H A ) ) |
|
3 | 1 2 | sseqtrd | |- ( ( A e. SH /\ B e. SH ) -> A C_ ( B +H A ) ) |