Theorem cmm2i

Description: A Hilbert lattice element commutes with its meet. (Contributed by NM, 7-Aug-2004) (New usage is discouraged.)

	Ref	Expression
Hypotheses	pjoml2.1	⊢ 𝐴 ∈ Cℋ
	pjoml2.2	⊢ 𝐵 ∈ Cℋ
Assertion	cmm2i	⊢ 𝐵 𝐶ℋ ( 𝐴 ∩ 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		pjoml2.1	⊢ 𝐴 ∈ Cℋ
2		pjoml2.2	⊢ 𝐵 ∈ Cℋ
3	2 1	cmm1i	⊢ 𝐵 𝐶ℋ ( 𝐵 ∩ 𝐴 )
4		incom	⊢ ( 𝐵 ∩ 𝐴 ) = ( 𝐴 ∩ 𝐵 )
5	3 4	breqtri	⊢ 𝐵 𝐶ℋ ( 𝐴 ∩ 𝐵 )