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 ∈ Cℋ
	qlaxr4.2	⊢ 𝐵 ∈ Cℋ
	qlaxr4.3	⊢ 𝐴 = 𝐵
Assertion	qlaxr4i	⊢ ( ⊥ ‘ 𝐴 ) = ( ⊥ ‘ 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		qlaxr4.1	⊢ 𝐴 ∈ Cℋ
2		qlaxr4.2	⊢ 𝐵 ∈ Cℋ
3		qlaxr4.3	⊢ 𝐴 = 𝐵
4	3	fveq2i	⊢ ( ⊥ ‘ 𝐴 ) = ( ⊥ ‘ 𝐵 )