let S be non empty non void ManySortedSign ; :: thesis: for U1 being non-empty MSAlgebra over S

for f being Element of MSAAut U1 holds f "" in MSAAut U1

let U1 be non-empty MSAlgebra over S; :: thesis: for f being Element of MSAAut U1 holds f "" in MSAAut U1

let f be Element of MSAAut U1; :: thesis: f "" in MSAAut U1

f is_isomorphism U1,U1 by Def5;

then f "" is_isomorphism U1,U1 by MSUALG_3:14;

hence f "" in MSAAut U1 by Def5; :: thesis: verum

for f being Element of MSAAut U1 holds f "" in MSAAut U1

let U1 be non-empty MSAlgebra over S; :: thesis: for f being Element of MSAAut U1 holds f "" in MSAAut U1

let f be Element of MSAAut U1; :: thesis: f "" in MSAAut U1

f is_isomorphism U1,U1 by Def5;

then f "" is_isomorphism U1,U1 by MSUALG_3:14;

hence f "" in MSAAut U1 by Def5; :: thesis: verum