Theorem qlaxr5i

Description: One of the conditions showing CH is an ortholattice. (This corresponds to axiom "ax-r5" in the Quantum Logic Explorer.) (Contributed by NM, 4-Aug-2004) (New usage is discouraged.)

	Ref	Expression
Hypotheses	qlaxr5.1	$$⊢A\in {\mathbf{C}}_{\mathscr{H}}$$
	qlaxr5.2	$$⊢B\in {\mathbf{C}}_{\mathscr{H}}$$
	qlaxr5.3	$$⊢C\in {\mathbf{C}}_{\mathscr{H}}$$
	qlaxr5.4	$$⊢A=B$$
Assertion	qlaxr5i	$$⊢A{\vee }_{\mathscr{H}}C=B{\vee }_{\mathscr{H}}C$$

Proof

Step	Hyp	Ref	Expression
1		qlaxr5.1	$$⊢A\in {\mathbf{C}}_{\mathscr{H}}$$
2		qlaxr5.2	$$⊢B\in {\mathbf{C}}_{\mathscr{H}}$$
3		qlaxr5.3	$$⊢C\in {\mathbf{C}}_{\mathscr{H}}$$
4		qlaxr5.4	$$⊢A=B$$
5	4	oveq1i	$$⊢A{\vee }_{\mathscr{H}}C=B{\vee }_{\mathscr{H}}C$$