code to build systems of equations

Question

I asked the question before but I forgot my login information:

here is the question: How many equation systems can I build from five equations?

the code works good but miss some equations for example if we have A1,A2,A3,A4 the code will give us

 {A1 == A2 && A2 == A3},
 {A1 == A2 && A2 == A4},
 {A1 == A3 && A3 == A4},
 {A2 == A3 && A3 == A4}

there are some systems lost like:

{A1 == A2 && A3 == A4},
{A1 == A3 && A2 == A4},
{A1 == A4 && A2 == A3}

Can anyone help me and fix the code so we can find all systems.

Thank you