Theorem cmcm2ii

Description: Commutation with orthocomplement. Theorem 2.3(i) of Beran p. 39. (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	cmcm2ii	|- 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	cmcm2i	|- ( A C_H B <-> A C_H ( _|_ ` B ) )
5	3 4	mpbi	|- A C_H ( _|_ ` B )