It's the total wavefunction that must be antisymmetric. This includes both the position and the spin (and any other degrees of freedom that may be present, like isospin). So for example a spin up fermion and a spin down fermion can have the same X.
You're mistaken, hokhani. Since you don't believe me, take a look at the Slater Determinant page in Wikipedia. There it says, "The Slater determinant arises from the consideration of a wave function for a collection of electrons, each with a wave function known as the spin-orbital, χ(x), where x denotes the position and spin of the singular electron."
Your reference may be doing the same thing: letting the notation x stand for both spin and position combined.
Thanks very much
As i found out, there are 3 factors determining the pauli exclusion principal:
1) Particles' positions(x,y,z)
2) Particles' spins
3) Particles' energy states
Would you tell me if i am wrong?