MHB Creating theorems from the given axioms

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Given the following axioms, create 3 theorems.

Axiom 1: Each game is played by two distinct teams.
Axiom 2: There are at least four teams.
Axiom 3: At least six games are played.
Axiom 4: Each team plays at most four games.

I have already proven each axioms independence.

These are the following theorems I have:
1. There are at least 2 teams that play a game
2. If there are exactly 4 teams then there at most 8 games

I have completely proven theorem 1. I just need help proving theorem 2 and creating/proving a third theorem.

Any help will be greatly appreciated!
 
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Hello and welcome to MHB, dezzi! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?
 

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