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Metamath Proof Explorer
Description: The class of all complex Hilbert spaces is a relation. (Contributed by NM, 17-Mar-2007) (New usage is discouraged.)
|
|
Ref |
Expression |
|
Assertion |
hlrel |
⊢ Rel CHilOLD |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
hlobn |
⊢ ( 𝑥 ∈ CHilOLD → 𝑥 ∈ CBan ) |
| 2 |
1
|
ssriv |
⊢ CHilOLD ⊆ CBan |
| 3 |
|
bnrel |
⊢ Rel CBan |
| 4 |
|
relss |
⊢ ( CHilOLD ⊆ CBan → ( Rel CBan → Rel CHilOLD ) ) |
| 5 |
2 3 4
|
mp2 |
⊢ Rel CHilOLD |