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

now :: thesis: for a, b, c being Element of F₁() holds f1 . (a,b,c) = f2 . (a,b,c)

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

end;

hence f1 = f2 by MULTOP_1:3; :: thesis: verum