Electronic – Compare two voltages and output the lower of the two

I am working on a circuit that is connected to a 10V supply (can supply about 1-2mA).

We have two signals, let's call them S1 and S2.
We also have an input to the circuit called IN1.

My goal here is to compare the two signals, S1 and S2 (They may range from 0 to 10V) and output the LOWER of the two into the circuit's IN1 pin.

What makes this challenging is the fact that the LOWER voltage needs to be output.

I can easily make a microcontroller compare two voltages on the A/D pins and output the lower on the D/A pin, but i'm afraid 2mA of power will not be enough to run the microcontroller properly – plus i'm sure there must be a much easier way.

EDIT: According to the simulation, accepted solution works like a charm! OpAmp source current is important in order to make sure it doesn't go past the current limit. Proper selection of OpAmp also allows OUT to be very close to V- (0V in this case).

I simulated this in LTSpice with a LT1490A OpAmp and a 22K resistor instead of a 1K.

To simulate i simply chose IN1 as 5V and varied IN2 from 0 to 10V. The results should be quite clear and self-explanatory. V1 (not shown below) and V2 are my V+ and V-. These are 10V and 0V.