In my textbook it says for an ideal gas, as volume decreases at constant pressure, there is a decrease in temperature. At first, I fully agreed because as volume decreases the temperature decreases by the gas laws, but then when I tried to apply $P\times{\Delta{V}}$ to the process, it appears that $\Delta{U}$ increases as the volume decreases, which does make sense since decreases volume at constant pressure should intuitively increase some type of energy; in this case internal energy.
Obviously, this is my faulty reasoning but the contradiction arises when one takes not that if $\Delta{U}$ is positive, then $\Delta{T}$ is positive as well. This tells us that T increases.
Where did my reasoning go wrong and what is the correct way of view this isobaric process?
EDIT:
So, when looking at Greiner Neise thermodynamics and statistical mechanics, the general equation is reported as:
$\ dH|_p = \delta Q|_p + \delta W^{rev}_{other}|_p$
Where the $\ W^{rev}_{other}$ is utilizable work, not simply volume work against the constant external pressure.
I apologize, I wanted to edit my own but edited this instead. Please remove if not suitable.