Description: The closed subspace zero is the smallest member of CH . (Contributed by NM, 15-Oct-1999) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypothesis | ch0le.1 | ⊢ 𝐴 ∈ Cℋ | |
Assertion | ch0lei | ⊢ 0ℋ ⊆ 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ch0le.1 | ⊢ 𝐴 ∈ Cℋ | |
2 | ch0le | ⊢ ( 𝐴 ∈ Cℋ → 0ℋ ⊆ 𝐴 ) | |
3 | 1 2 | ax-mp | ⊢ 0ℋ ⊆ 𝐴 |