Theorem qlaxr4i

Description: One of the conditions showing CH is an ortholattice. (This corresponds to axiom "ax-r4" in the Quantum Logic Explorer.) (Contributed by NM, 4-Aug-2004) (New usage is discouraged.)

	Ref	Expression
Hypotheses	qlaxr4.1	$$⊢A\in {\mathbf{C}}_{\mathscr{H}}$$
	qlaxr4.2	$$⊢B\in {\mathbf{C}}_{\mathscr{H}}$$
	qlaxr4.3	$$⊢A=B$$
Assertion	qlaxr4i	$$⊢\perp \left(A\right)=\perp \left(B\right)$$

Proof

Step	Hyp	Ref	Expression
1		qlaxr4.1	$$⊢A\in {\mathbf{C}}_{\mathscr{H}}$$
2		qlaxr4.2	$$⊢B\in {\mathbf{C}}_{\mathscr{H}}$$
3		qlaxr4.3	$$⊢A=B$$
4	3	fveq2i	$$⊢\perp \left(A\right)=\perp \left(B\right)$$