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
A1: for x, y being Real holds f1 . x,y = min x,y and
A2: 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 & f2 . x,y = min x,y ) by A1, A2;
hence f1 . x,y = f2 . x,y ; :: thesis: verum

end;

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