let T, S be 1-sorted ; :: thesis: for f being Function of T,S st rng f = [#] S & f is one-to-one holds
f " is one-to-one
let f be Function of T,S; :: thesis: ( rng f = [#] S & f is one-to-one implies f " is one-to-one )
assume that
A1: rng f = [#] S and
A2: f is one-to-one ; :: thesis: f " is one-to-one
A3: f is onto by A1, FUNCT_2:def 3;
f " is one-to-one by A2;
hence f " is one-to-one by A2, A3, Def4; :: thesis: verum