Description: Meet with lattice one in CH . (Contributed by NM, 24-Oct-1999) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypothesis | ch0le.1 | ⊢ 𝐴 ∈ Cℋ | |
Assertion | chm1i | ⊢ ( 𝐴 ∩ ℋ ) = 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ch0le.1 | ⊢ 𝐴 ∈ Cℋ | |
2 | 1 | chssii | ⊢ 𝐴 ⊆ ℋ |
3 | df-ss | ⊢ ( 𝐴 ⊆ ℋ ↔ ( 𝐴 ∩ ℋ ) = 𝐴 ) | |
4 | 2 3 | mpbi | ⊢ ( 𝐴 ∩ ℋ ) = 𝐴 |