Theorem qlaxr5i

Description: One of the conditions showing CH is an ortholattice. (This corresponds to axiom "ax-r5" in the Quantum Logic Explorer.) (Contributed by NM, 4-Aug-2004) (New usage is discouraged.)

	Ref	Expression
Hypotheses	qlaxr5.1	⊢ 𝐴 ∈ Cℋ
	qlaxr5.2	⊢ 𝐵 ∈ Cℋ
	qlaxr5.3	⊢ 𝐶 ∈ Cℋ
	qlaxr5.4	⊢ 𝐴 = 𝐵
Assertion	qlaxr5i	⊢ ( 𝐴 ∨ℋ 𝐶 ) = ( 𝐵 ∨ℋ 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		qlaxr5.1	⊢ 𝐴 ∈ Cℋ
2		qlaxr5.2	⊢ 𝐵 ∈ Cℋ
3		qlaxr5.3	⊢ 𝐶 ∈ Cℋ
4		qlaxr5.4	⊢ 𝐴 = 𝐵
5	4	oveq1i	⊢ ( 𝐴 ∨ℋ 𝐶 ) = ( 𝐵 ∨ℋ 𝐶 )