Why is the Latent heat of solid to gas equal to the sum of latent heat of solid to liquid and the latent heat of liquid to gas?

Question

What is the mathematical reason as to why the following is through at the triple point temperature $T_3$?

$$ L_{solid -> gas} = L_{solid -> liquid} + L_{liquid -> gas}$$

Where $L$ is latent heat.

I tried convincing myself through the idea of state functions of the system, where only the final and initial states matters. However, I ran into a problem because latent heat $L$ is effectively the heat abosrbed during a change of state, however, heat $Q$ is not a state function itself.

Answer 1

A good explanation , why enthalpy $\Delta H$ is a state function, is because $\Delta H = \Delta U - \Delta (pV)$. Notice that the functions on the right are state functions. Hence, enthalpy is a state function.

So this means if the system changes state from a given set of pressure, volume and temperature variables ,to another, enthalpy is always same for the same state change.