reserve X for set,
        A for Subset of X,
        R,S for Relation of X;
reserve QUS for Quasi-UniformSpace;
reserve SUS for Semi-UniformSpace;

theorem Th16:
  for US being non empty axiom_U1 UniformSpaceStr,
  x being Element of US,
  V being Element of the entourages of US holds x in Neighborhood(V,x)
  proof
    let US be non empty axiom_U1 UniformSpaceStr,
    x be Element of US,
    V be Element of the entourages of US;
    US is axiom_U1; then
A1: id the carrier of US c= V;
    [x,x] in id the carrier of US by RELAT_1:def 10;
    hence thesis by A1;
  end;
