Consider the following diagram for a binary liquid system comprised of A and B, where A is the more volatile component.
My professor says
Consider an isopleth from $a$ to $a_4$. At the start, the solution is in pure liquid phase at state $a$.
As we reduce the pressure, the solution starts to boil at $a_1$. The composition of the liquid solution is denoted by the point $a_1$ which is the same as the overall composition of the solution since the solution has only just started to boil. The composition of the first trace of vapor formed is $a_1'$.
As the we reduce the pressure, the solution continues to boil to reach point $a_2''$. We may draw a tie line to find the composition of the liquid $a_2$ and the composition of the vapor $a_2'$. At every pressure where the solution exists as a mixture of liquid and vapor, we may use a tie line to find out its composition in the liquid and vapor phase.
Upon reaching $a_3'$, the solution has just been completely changed into vapor phase and the last trace of liquid has the composition $a_3$. After all the solution is vaporized at $a_4$, the composition of the vapor is again the overall composition of the solution.
I am slightly confused about we are able to make the pressure drop from $a_1$ to $a_3'$. My reasoning is: since the liquid and vapor are in equilibrium, shouldn't enough liquid keep on evaporating to maintain a constant vapor pressure?