Theorem qlaxr2i

Description: One of the conditions showing CH is an ortholattice. (This corresponds to axiom "ax-r2" in the Quantum Logic Explorer.) (Contributed by NM, 4-Aug-2004) (New usage is discouraged.)

	Ref	Expression
Hypotheses	qlaxr2.1	$$⊢A\in {\mathbf{C}}_{\mathscr{H}}$$
	qlaxr2.2	$$⊢B\in {\mathbf{C}}_{\mathscr{H}}$$
	qlaxr2.3	$$⊢C\in {\mathbf{C}}_{\mathscr{H}}$$
	qlaxr2.4	$$⊢A=B$$
	qlaxr2.5	$$⊢B=C$$
Assertion	qlaxr2i	$$⊢A=C$$

Proof

Step	Hyp	Ref	Expression
1		qlaxr2.1	$$⊢A\in {\mathbf{C}}_{\mathscr{H}}$$
2		qlaxr2.2	$$⊢B\in {\mathbf{C}}_{\mathscr{H}}$$
3		qlaxr2.3	$$⊢C\in {\mathbf{C}}_{\mathscr{H}}$$
4		qlaxr2.4	$$⊢A=B$$
5		qlaxr2.5	$$⊢B=C$$
6	4 5	eqtri	$$⊢A=C$$