A constraint consists of a base parameter and a one or more dependent (or constrained) parameters. In the equality constraint the first parameter specified is the base parameter. When minimising the fitting system only works with free parameters, where free is defined as both not frozen and not constrained. The system ensures that the constraints are obeyed at all times.
The effect of placing constrains on model parameter values is to reduce the number of degrees of freedom in the fit - consequently the size of confidence regions produced by SERROR will change from those of the equivalent unconstrained fit.