Who proved the modern form of the [fundamental theorem of Galois theory?](http://en.wikipedia.org/wiki/Fundamental_theorem_of_Galois_theory). Was it in the original Galois' manuscript?



The fundamental theorem of Galois theory
Galois's Proposition I (as translated by Edwards) is:


Let the equation be given whose $m$ roots are $a,b,c,\ldots$. There will always be a group of permuations of the letters $a,b,c,\ldots$ which will have the following property: 1) that each function invariant under the substitutions of this group will be known rationally; 2) conversely, that every function of these roots which can be determined rationally will be invariant under these substitutions. 


As Edwards observes, it takes a lot of work to decipher the exact meanings of "substitution" and "invariant" here, but once you've done that, this can be translated into modern language as:


If an element of the splitting field of $K(a,b,c,\ldots)$ is left fixed by all the automorphisms of the Galois group then it is in $K$.


The fundamental theorem of Galois theory (i.e. the Galois correspondence) follows easily, though Edwards doesn't say who first stated it.


