Yes.The 4 equations are from different people but maxwell was the one who proved that a relation existed between the quantities in those equations.Moreover if these equations are solved for dielectric medium,then the wave equation obtained also clearly indicates that
electromagnetic waves travel at speed of light.This is where maxwell got the target.The permittivity(epsilon)
and magnetic permeability(mu) were prior to maxwell not related to each other.but maxwell showed that velocity of EM waves is
c=1/squareroot(mu*epsilon).