Math Logic Proving Proofs

Give a proof of

http://www.earlham.edu/%7Epeters/writing/syncon.gif A ^ (A V B) http://www.earlham.edu/%7Epeters/writing/matequiv.gif A.

I have an additional question. I do not really understand what http://www.earlham.edu/%7Epeters/writing/syncon.gif means, as sometimes I have seen it placed in the middle of proofs and sometimes I see it has no influence to the answer to the question at all.

A ^ (AVB)

By Golden Rule

=> A http://www.earlham.edu/%7Epeters/writing/matequiv.gif A V B http://www.earlham.edu/%7Epeters/writing/matequiv.gif A V A V B

By Idempotency of V

=> A http://www.earlham.edu/%7Epeters/writing/matequiv.gif A V B http://www.earlham.edu/%7Epeters/writing/matequiv.gif A V B

By symmetry of http://www.earlham.edu/%7Epeters/writing/matequiv.gif

=> A

I need a lot of clarification for these steps as they do not make sense to me. I understand the last part of every step, but do not understand the rest of it.