Theorem qlax2i

Description: One of the equations showing CH is an ortholattice. (This corresponds to axiom "ax-2" 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	$$⊢B\in {\mathbf{C}}_{\mathscr{H}}$$
Assertion	qlax2i	$$⊢A{\vee }_{\mathscr{H}}B=B{\vee }_{\mathscr{H}}A$$

Proof

Step	Hyp	Ref	Expression
1		qlax.1	$$⊢A\in {\mathbf{C}}_{\mathscr{H}}$$
2		qlax.2	$$⊢B\in {\mathbf{C}}_{\mathscr{H}}$$
3	1 2	chjcomi	$$⊢A{\vee }_{\mathscr{H}}B=B{\vee }_{\mathscr{H}}A$$