Theorem qlax4i

Description: One of the equations showing CH is an ortholattice. (This corresponds to axiom "ax-4" in the Quantum Logic Explorer.) (Contributed by NM, 4-Aug-2004) (New usage is discouraged.)

	Ref	Expression
Hypotheses	qlax.1	|- A e. CH
	qlax.2	|- B e. CH
Assertion	qlax4i	|- ( A vH ( B vH ( _|_ ` B ) ) ) = ( B vH ( _|_ ` B ) )

Proof

Step	Hyp	Ref	Expression
1		qlax.1	|- A e. CH
2		qlax.2	|- B e. CH
3	1	chj1i	|- ( A vH ~H ) = ~H
4	2	chjoi	|- ( B vH ( _|_ ` B ) ) = ~H
5	4	oveq2i	|- ( A vH ( B vH ( _|_ ` B ) ) ) = ( A vH ~H )
6	3 5 4	3eqtr4i	|- ( A vH ( B vH ( _|_ ` B ) ) ) = ( B vH ( _|_ ` B ) )