let f1, f2 be BinOp of REAL; :: thesis: ( ( for x, y being Real holds f1 . (x,y) = min (x,y) ) & ( for x, y being Real holds f2 . (x,y) = min (x,y) ) implies f1 = f2 )
assume that
A2: for x, y being Real holds f1 . (x,y) = min (x,y) and
A3: for x, y being Real holds f2 . (x,y) = min (x,y) ; :: thesis: f1 = f2
for x, y being Element of REAL holds f1 . (x,y) = f2 . (x,y)

proof

let x, y be Element of REAL ; :: thesis: f1 . (x,y) = f2 . (x,y)
f1 . (x,y) = min (x,y) by A2;
hence f1 . (x,y) = f2 . (x,y) by A3; :: thesis: verum

end;

hence f1 = f2 by BINOP_1:2; :: thesis: verum