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	$$⊢A\in {\mathbf{C}}_{\mathscr{H}}$$
	qlaxr1.2	$$⊢B\in {\mathbf{C}}_{\mathscr{H}}$$
	qlaxr1.3	$$⊢A=B$$
Assertion	qlaxr1i	$$⊢B=A$$

Proof

Step	Hyp	Ref	Expression
1		qlaxr1.1	$$⊢A\in {\mathbf{C}}_{\mathscr{H}}$$
2		qlaxr1.2	$$⊢B\in {\mathbf{C}}_{\mathscr{H}}$$
3		qlaxr1.3	$$⊢A=B$$
4	3	eqcomi	$$⊢B=A$$