Description: Real closure of inner product with self. (Contributed by NM, 29-May-1999) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Assertion | hiidrcl | |- ( A e. ~H -> ( A .ih A ) e. RR ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid | |- ( A .ih A ) = ( A .ih A ) |
|
2 | hire | |- ( ( A e. ~H /\ A e. ~H ) -> ( ( A .ih A ) e. RR <-> ( A .ih A ) = ( A .ih A ) ) ) |
|
3 | 1 2 | mpbiri | |- ( ( A e. ~H /\ A e. ~H ) -> ( A .ih A ) e. RR ) |
4 | 3 | anidms | |- ( A e. ~H -> ( A .ih A ) e. RR ) |