Circuit diagram of op amp
Q5/Q6 could just as easily be a darlington and it would work fine although it would slightly reduce the maximum negative output swing as it would saturate at a slightly higher (less negative) voltage.

Usually the diode labeled as Q3 would be a diode configured transistor which then, with Q4, forms a matched current mirror. This current mirror then acts to keep the currents just about equal to each other in the collectors of Q1,Q3 and Q4.


A DC signal between the opamp's inputs, where V1 is less than V2, results in Vbe of Q2 being greater than the Vbe of Q1 which results in a larger current out of the collector of Q2 than those currents being held equal to each other in the collectors of Q1,Q3 and Q4.
The extra current in Q2 must be pushed down the connection to the base of Q5 which saturates the output stage negatively because of the high combined gain of Q5 &amp; Q6.
So you always need to consider the signal between the first and second stages as a current signal, the voltage at the base of Q5 is held just about constant at about 1.4V with only a slight ripple on it of a couple of mV or so.
For an ac situation when feedback is added. The alternating difference between the inputs pushes and pulls an ac current through the compensation capacitor,Cc into and out of the input stage.