Theorem cmcmii

Description: Commutation is symmetric. Theorem 2(v) of Kalmbach p. 22. (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	cmcmii	|- B C_H A

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	cmcmi	|- ( A C_H B <-> B C_H A )
5	3 4	mpbi	|- B C_H A