reserve k,m,n for Nat, kk,mm,nn for Element of NAT, X,Y,x,y,z for set;
reserve S,S1,S2 for Language, s,s1,s2 for Element of S;

theorem (AtomicFormulaSymbolsOf S) \ OwnSymbolsOf S={TheEqSymbOf S}
proof
set o=the OneF of S, z=the ZeroF of S, f=the adicity of S, R=RelSymbolsOf S,
O=OwnSymbolsOf S, SS=AllSymbolsOf S, e=TheEqSymbOf S, n=TheNorSymbOf S,
A=AtomicFormulaSymbolsOf S, D = (the carrier of S) \ {o};
A1: e in A by Lm3;
A\O =
A \ (A \ {z})
by XBOOLE_1:41 .= (A \ A) \/ (A /\ {z}) by XBOOLE_1:52
.= {z} by ZFMISC_1:46, A1; hence thesis;
end;
