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	$$⊢A\in {\mathbf{C}}_{\mathscr{H}}$$
	qlax.2	$$⊢B\in {\mathbf{C}}_{\mathscr{H}}$$
	qlax.3	$$⊢C\in {\mathbf{C}}_{\mathscr{H}}$$
Assertion	qlax3i	$$⊢\left(A{\vee }_{\mathscr{H}}B\right){\vee }_{\mathscr{H}}C=A{\vee }_{\mathscr{H}}\left(B{\vee }_{\mathscr{H}}C\right)$$

Proof

Step	Hyp	Ref	Expression
1		qlax.1	$$⊢A\in {\mathbf{C}}_{\mathscr{H}}$$
2		qlax.2	$$⊢B\in {\mathbf{C}}_{\mathscr{H}}$$
3		qlax.3	$$⊢C\in {\mathbf{C}}_{\mathscr{H}}$$
4	1 2 3	chjassi	$$⊢\left(A{\vee }_{\mathscr{H}}B\right){\vee }_{\mathscr{H}}C=A{\vee }_{\mathscr{H}}\left(B{\vee }_{\mathscr{H}}C\right)$$