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 ∈ Cℋ
	qlaxr2.2	⊢ 𝐵 ∈ Cℋ
	qlaxr2.3	⊢ 𝐶 ∈ Cℋ
	qlaxr2.4	⊢ 𝐴 = 𝐵
	qlaxr2.5	⊢ 𝐵 = 𝐶
Assertion	qlaxr2i	⊢ 𝐴 = 𝐶

Proof

Step	Hyp	Ref	Expression
1		qlaxr2.1	⊢ 𝐴 ∈ Cℋ
2		qlaxr2.2	⊢ 𝐵 ∈ Cℋ
3		qlaxr2.3	⊢ 𝐶 ∈ Cℋ
4		qlaxr2.4	⊢ 𝐴 = 𝐵
5		qlaxr2.5	⊢ 𝐵 = 𝐶
6	4 5	eqtri	⊢ 𝐴 = 𝐶