
theorem Th18:
for S being Ring,
    R being Subring of S
for x,y being Element of S,
    x1,y1 being Element of R st x = x1 & y = y1 holds x * y = x1 * y1
proof
let R be Ring, S being Subring of R;
let x,y be Element of R, x1,y1 be Element of S;
set C1 = the carrier of S;
the multF of S = (the multF of R) || C1 by C0SP1:def 3;
hence thesis by FUNCT_1:49,ZFMISC_1:87;
end;
