Pauli principle ($P_{12}\Psi =-\Psi$)

The complete wavefunction of identical fermions changes sign on exchange of two particles, including their spatial and internal coordinates. The Pauli exclusion principle follows because an antisymmetrized product with two identical complete spin orbitals is zero. Antisymmetry concerns the total state; a spin-antisymmetric singlet state can have a symmetric spatial factor.