Description: Membership in subspace sum. (Contributed by NM, 19-Oct-1999) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypotheses | ch0le.1 | |- A e. CH |
|
chjcl.2 | |- B e. CH |
||
Assertion | chseli | |- ( C e. ( A +H B ) <-> E. x e. A E. y e. B C = ( x +h y ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ch0le.1 | |- A e. CH |
|
2 | chjcl.2 | |- B e. CH |
|
3 | 1 | chshii | |- A e. SH |
4 | 2 | chshii | |- B e. SH |
5 | 3 4 | shseli | |- ( C e. ( A +H B ) <-> E. x e. A E. y e. B C = ( x +h y ) ) |