consider f being Function such that
A1: ( dom f = F₁() & ( for x being object st x in F₁() holds
f . x = F₂(x) ) ) from FUNCT_1:sch 3();
take f ; :: thesis: ( dom f = F₁() & ( for g being Function st g in F₁() holds
f . g = F₂(g) ) )
thus ( dom f = F₁() & ( for g being Function st g in F₁() holds
f . g = F₂(g) ) ) by A1; :: thesis: verum