Theorem qlax3i

Description: One of the equations showing CH is an ortholattice. (This corresponds to axiom "ax-3" in the Quantum Logic Explorer.) (Contributed by NM, 4-Aug-2004) (New usage is discouraged.)

	Ref	Expression
Hypotheses	qlax.1	⊢ 𝐴 ∈ Cℋ
	qlax.2	⊢ 𝐵 ∈ Cℋ
	qlax.3	⊢ 𝐶 ∈ Cℋ
Assertion	qlax3i	⊢ ( ( 𝐴 ∨ℋ 𝐵 ) ∨ℋ 𝐶 ) = ( 𝐴 ∨ℋ ( 𝐵 ∨ℋ 𝐶 ) )

Proof

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