let f1, f2 be UnOp of F₁(); :: thesis: ( ( for a being Element of F₁() holds f1 . a = F₂(a) ) & ( for a being Element of F₁() holds f2 . a = F₂(a) ) implies f1 = f2 )
assume that
A1: for a being Element of F₁() holds f1 . a = F₂(a) and
A2: for a being Element of F₁() holds f2 . a = F₂(a) ; :: thesis: f1 = f2

now

let a be Element of F₁(); :: thesis: f1 . a = f2 . a
thus f1 . a = F₂(a) by A1
.= f2 . a by A2 ; :: thesis: verum

end;

hence f1 = f2 by FUNCT_2:113; :: thesis: verum