special relativity - Given the 1st Postulate of SR, doesn't the 2nd Postulate go without saying?

i've been looking over possible duplicates of this question and haven't found one yet.

so, using Wikipedia as the textual source:

1. 
   

   The Principle of Relativity – The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems in uniform translatory motion relative to each other.

   
   
   


2. 
   

   The Principle of Invariant Light Speed – "... light is always propagated in empty space with a definite velocity [speed] $c$ which is independent of the state of motion of the emitting body". That is, light in vacuum propagates with the speed $c$ (a fixed constant, independent of direction) in at least one system of inertial coordinates (the "stationary system"), regardless of the state of motion of the light source.

   
   

so, is it not the case that observers in "one or the other of two systems in uniform translatory motion relative to each other" have the very same $\epsilon_0$ and $\mu_0$? if they don't, that contradicts the premise of the 1st Postulate.

i just cannot see how the 2nd Postulate is not redundant. it comes about directly from the 1st and from the known laws of physics preceding SR.

you see, it's not just about light and $c$ and $\epsilon_0$ and $\mu_0$. it's all the other laws of physics and the parameters that come with these laws. i.e. every inertial frame of reference has the same Planck's constant, $\hbar$, same gravitational constant, $G$, and same elementary charge $e$. if the frames of reference didn't have the same values, such would violate the 1st Postulate, but that wouldn't violate the 2nd Postulate since that's restricted to $c$.