speed of light - Is the second postulate of Einstein's special relativity an axiom?

I'm trying to grasp Einstein's special relativity theory and can't seem to find a clear answer as to why Einstein concluded that the speed of light is constant to observers in different inertial frames.

1. 
   

   Sometimes I read it's because of the Michelson-Morley experiment. But that only proves there's no aether/medium for light to travel through.

   
   


2. 
   

   Sometimes I read that he derived it from Maxwell's equations. I still need to study those, so I can't judge about that.

   
   


3. 
   
   

   And sometimes I read that it's just an axiom that we need to accept.

   
   

So what's the right answer?