Theorem cmcm3ii

Description: Commutation with orthocomplement. Remark in Kalmbach p. 23. (Contributed by NM, 7-Aug-2004) (New usage is discouraged.)

	Ref	Expression
Hypotheses	pjoml2.1	|- A e. CH
	pjoml2.2	|- B e. CH
	cmcmi.1	|- A C_H B
Assertion	cmcm3ii	|- ( _|_ ` A ) C_H B

Proof

Step	Hyp	Ref	Expression
1		pjoml2.1	|- A e. CH
2		pjoml2.2	|- B e. CH
3		cmcmi.1	|- A C_H B
4	1 2	cmcm3i	|- ( A C_H B <-> ( _|_ ` A ) C_H B )
5	3 4	mpbi	|- ( _|_ ` A ) C_H B