axiomatic system - creating theorems

Consider the following axiomatic system:

Axiom 1: Each game is played by two distinct teams

Axiom 2: There are at least four teams

Axiom 3: There are at least six games played

Axiom 4: Each team played at most 4 games.

1.      Expand your axiomatic system from part A by doing the following:

a.       Create two theorems that follow from the four axioms.

b.      Prove each theorem from part (a) using any of the four axioms and/or any of the theorems from part (a) that you have already proven.