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