set E = { a where a is Element of U0 : ex o being operation of U0 st
( arity o = 0 & a in rng o ) } ;
{ a where a is Element of U0 : ex o being operation of U0 st
( arity o = 0 & a in rng o ) } c= the carrier of U0

proof

let x be object ; :: according to TARSKI:def 3 :: thesis: ( not x in { a where a is Element of U0 : ex o being operation of U0 st
( arity o = 0 & a in rng o ) } or x in the carrier of U0 )
assume x in { a where a is Element of U0 : ex o being operation of U0 st
( arity o = 0 & a in rng o ) } ; :: thesis: x in the carrier of U0
then ex w being Element of U0 st
( w = x & ex o being operation of U0 st
( arity o = 0 & w in rng o ) ) ;
hence x in the carrier of U0 ; :: thesis: verum

end;

hence { a where a is Element of U0 : ex o being operation of U0 st
( arity o = 0 & a in rng o ) } is Subset of U0 ; :: thesis: verum