Theorem qlaxr1i

Description: One of the conditions showing CH is an ortholattice. (This corresponds to axiom "ax-r1" in the Quantum Logic Explorer.) (Contributed by NM, 4-Aug-2004) (New usage is discouraged.)

	Ref	Expression
Hypotheses	qlaxr1.1	⊢ 𝐴 ∈ Cℋ
	qlaxr1.2	⊢ 𝐵 ∈ Cℋ
	qlaxr1.3	⊢ 𝐴 = 𝐵
Assertion	qlaxr1i	⊢ 𝐵 = 𝐴

Proof

Step	Hyp	Ref	Expression
1		qlaxr1.1	⊢ 𝐴 ∈ Cℋ
2		qlaxr1.2	⊢ 𝐵 ∈ Cℋ
3		qlaxr1.3	⊢ 𝐴 = 𝐵
4	3	eqcomi	⊢ 𝐵 = 𝐴