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 𝐴C
Assertion qlax1i 𝐴 = ( ⊥ ‘ ( ⊥ ‘ 𝐴 ) )

Proof

Step Hyp Ref Expression
1 qlax1.1 𝐴C
2 1 ococi ( ⊥ ‘ ( ⊥ ‘ 𝐴 ) ) = 𝐴
3 2 eqcomi 𝐴 = ( ⊥ ‘ ( ⊥ ‘ 𝐴 ) )