Theorem qlaxr2i

Description: One of the conditions showing CH is an ortholattice. (This corresponds to axiom "ax-r2" in the Quantum Logic Explorer.) (Contributed by NM, 4-Aug-2004) (New usage is discouraged.)

	Ref	Expression
Hypotheses	qlaxr2.1	|- A e. CH
	qlaxr2.2	|- B e. CH
	qlaxr2.3	|- C e. CH
	qlaxr2.4	|- A = B
	qlaxr2.5	|- B = C
Assertion	qlaxr2i	|- A = C

Proof

Step	Hyp	Ref	Expression
1		qlaxr2.1	|- A e. CH
2		qlaxr2.2	|- B e. CH
3		qlaxr2.3	|- C e. CH
4		qlaxr2.4	|- A = B
5		qlaxr2.5	|- B = C
6	4 5	eqtri	|- A = C