Metamath Proof Explorer


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 e. CH
qlaxr1.2
|- B e. CH
qlaxr1.3
|- A = B
Assertion qlaxr1i
|- B = A

Proof

Step Hyp Ref Expression
1 qlaxr1.1
 |-  A e. CH
2 qlaxr1.2
 |-  B e. CH
3 qlaxr1.3
 |-  A = B
4 3 eqcomi
 |-  B = A