let R be comRing; :: thesis: for M being LeftMod of R holds canHom M is unity-preserving
let M be LeftMod of R; :: thesis: canHom M is unity-preserving
consider f being Endomorphism of R,M such that
A1: ( f = (curry the lmult of M) . (1. R) & (canHom M) . (1. R) = AbGr f ) by Def27;
f = 1_End M

proof

for m being Element of M holds f . m = (1_End M) . m

proof

let m be Element of M; :: thesis: f . m = (1_End M) . m
f . m = (1. R) * m by A1, LOPBAN_8:7
.= (1_End M) . m ;
hence f . m = (1_End M) . m ; :: thesis: verum

end;

hence f = 1_End M by FUNCT_2:63; :: thesis: verum

end;

hence canHom M is unity-preserving by A1, Lm37; :: thesis: verum