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

proof

let a, b, c be Element of B; :: thesis: f1 . (a,b,c) = f2 . (a,b,c)
f1 . (a,b,c) = Ros (a,b,c) by A1
.= f2 . (a,b,c) by A2 ;
hence f1 . (a,b,c) = f2 . (a,b,c) ; :: thesis: verum

end;

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