Metamath Proof Explorer


Theorem qlax1i

Description: One of the equations showing CH is an ortholattice. (This corresponds to axiom "ax-1" in the Quantum Logic Explorer.) (Contributed by NM, 4-Aug-2004) (New usage is discouraged.)

Ref Expression
Hypothesis qlax1.1
|- A e. CH
Assertion qlax1i
|- A = ( _|_ ` ( _|_ ` A ) )

Proof

Step Hyp Ref Expression
1 qlax1.1
 |-  A e. CH
2 1 ococi
 |-  ( _|_ ` ( _|_ ` A ) ) = A
3 2 eqcomi
 |-  A = ( _|_ ` ( _|_ ` A ) )