Need math help with axiomatic systems and theorems

Given the following axioms: 

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. I need help developing a third theorem and verifying the second is true. Theorem 1: If there are exactly 4 teams, then there are at most 8 games. Theorem 2: If there are exactly 6 games, then there are at most 12 teams. Theorem 3: