# Quantum field theory meson scattering calculation (scalar yukawa theory)

Please see this question for a clear background of the notation I use. My issue is that I want to use Wick's theorem to calculate the amplitude of meson $\psi(p_1)\psi(p_2)\rightarrow\psi(p_1')\psi(p_2')$ scattering. I can quickly get to the point where I need to evaluate:

$\langle p_1',p_2'|:\psi_1^\dagger\psi_1\psi_2^\dagger\psi_2:|p_1,p_2\rangle$

In my notes, the next step is

$\langle p_1',p_2'|:\psi_1^\dagger\psi_1\psi_2^\dagger\psi_2:|p_1,p_2\rangle=\langle p_1',p_2'|\psi_1^\dagger\psi_2^\dagger|0\rangle\langle0|\psi_1\psi_2|p_1,p_2\rangle$

where he seems to have changed orders of the fields and inserted $|0\rangle\langle0|$, $|0\rangle$ being the vacuum of the free theory. Can anyone explain what this particular step is? From thereafter the derivation is pretty clear to me

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