Theorem chm1i

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

Proof

Step	Hyp	Ref	Expression
1		ch0le.1	⊢ 𝐴 ∈ Cℋ
2	1	chssii	⊢ 𝐴 ⊆ ℋ
3		dfss2	⊢ ( 𝐴 ⊆ ℋ ↔ ( 𝐴 ∩ ℋ ) = 𝐴 )
4	2 3	mpbi	⊢ ( 𝐴 ∩ ℋ ) = 𝐴