Theorem chm1i

Description: Meet with lattice one in CH . (Contributed by NM, 24-Oct-1999) (New usage is discouraged.)

	Ref	Expression
Hypothesis	ch0le.1	$$⊢A\in {\mathbf{C}}_{\mathscr{H}}$$
Assertion	chm1i	$$⊢A\cap \mathscr{H}=A$$

Proof

Step	Hyp	Ref	Expression
1		ch0le.1	$$⊢A\in {\mathbf{C}}_{\mathscr{H}}$$
2	1	chssii	$$⊢A\subseteq \mathscr{H}$$
3		dfss2	$$⊢A\subseteq \mathscr{H}\leftrightarrow A\cap \mathscr{H}=A$$
4	2 3	mpbi	$$⊢A\cap \mathscr{H}=A$$