ex f being SetSequence of F₁() st
for n being Element of NAT holds f . n = F₃(n) from FUNCT_2:sch 4();
then consider f being SetSequence of F₁() such that
A1: for n being Element of NAT holds f . n = F₃(n) ;
for n being Nat holds f . n in F₂()

proof

let n be Nat; :: thesis: f . n in F₂()
n in NAT by ORDINAL1:def 12;
then f . n = F₃(n) by A1;
hence f . n in F₂() ; :: thesis: verum

end;

then rng f c= F₂() by NAT_1:52;
then reconsider f = f as SetSequence of F₂() by RELAT_1:def 19;
take f ; :: thesis: for n being Element of NAT holds f . n = F₃(n)
thus for n being Element of NAT holds f . n = F₃(n) by A1; :: thesis: verum