Theorem qlax5i

Description: One of the equations showing CH is an ortholattice. (This corresponds to axiom "ax-5" 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	qlax5i	|- ( A vH ( _|_ ` ( ( _|_ ` A ) vH B ) ) ) = A

Proof

Step	Hyp	Ref	Expression
1		qlax.1	|- A e. CH
2		qlax.2	|- B e. CH
3	1 2	chdmj2i	|- ( _|_ ` ( ( _|_ ` A ) vH B ) ) = ( A i^i ( _|_ ` B ) )
4	3	oveq2i	|- ( A vH ( _|_ ` ( ( _|_ ` A ) vH B ) ) ) = ( A vH ( A i^i ( _|_ ` B ) ) )
5	2	choccli	|- ( _|_ ` B ) e. CH
6	1 5	chabs1i	|- ( A vH ( A i^i ( _|_ ` B ) ) ) = A
7	4 6	eqtri	|- ( A vH ( _|_ ` ( ( _|_ ` A ) vH B ) ) ) = A