The network will see that there is a previous recorded transaction where you transferred those coins to someone else and so it will know you don't really have them.  Therefore it will reject your second transfer as invalid.  This is also how the network protects against someone just editing their wallet.dat file to give themselves a bunch of coins.

By the way, I don't suggest trying this as someone posted in another thread that they tried a similar thing as a test and ended up losing a bunch of coins in the process.  The network will not punish you for this (i.e. he did not lose his coins as a punishment) it was just some weird interaction between the client and the wallet file (the exact details elude me at the moment).

-Buck