Wave function of two different fermions

[Marchigno]

Hi! According to quantum field theory, must the wave function of two different fermions be antisymmetric?
If I have a state of two equal fermions: $$b^\dagger(p_1)b^\dagger(p_2)|0>$$ I can construct the general state of two fermions:
$$\int d^3p_1 d^3p_2f(p_1,p_2)b^\dagger(p_1)b^\dagger(p_2)|0>$$
where f is the wave function. Now because $$\{b^\dagger(p_1),b^\dagger(p_2)\}=0$$
the wave function f mast be antisymmetric.
The question is: if I now consider two different fermions: $$b^\dagger(p_1)d^\dagger(p_1)|0>$$
so that the general state is
$$\int d^3p_1 d^3p_2f(p_1,p_2)b^\dagger(p_1)d^\dagger(p_2)|0>$$
because
$$\{b^\dagger(p_1),d^\dagger(p_2)\}=0$$
remains true, does it mean the wave function of any two fermions will be antisymmetric? I thought it was true only for two identical particles!
Thank you for the answers! :)

 

[DrClaude]

If the fermion are not identical, then there is no possible symmetry to start with, so the Pauli principle does not apply.