This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.
Metamath Proof Explorer
Description: The class of all complex inner product spaces is a relation.
(Contributed by NM, 2-Apr-2007) (New usage is discouraged.)
|
|
Ref |
Expression |
|
Assertion |
phrel |
⊢ Rel CPreHilOLD |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
phnv |
⊢ ( 𝑥 ∈ CPreHilOLD → 𝑥 ∈ NrmCVec ) |
| 2 |
1
|
ssriv |
⊢ CPreHilOLD ⊆ NrmCVec |
| 3 |
|
nvrel |
⊢ Rel NrmCVec |
| 4 |
|
relss |
⊢ ( CPreHilOLD ⊆ NrmCVec → ( Rel NrmCVec → Rel CPreHilOLD ) ) |
| 5 |
2 3 4
|
mp2 |
⊢ Rel CPreHilOLD |