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;
reserve l,l1,l2 for literal Element of S, a for ofAtomicFormula Element of S,
r for relational Element of S, w,w1,w2 for string of S,
t,t1,t2 for termal string of S, tt,tt1, tt2 for Element of AllTermsOf S;
reserve phi0 for 0wff string of S;

theorem S-firstChar.phi0<>TheEqSymbOf S implies
phi0 is (OwnSymbolsOf S)-valued
proof
set O=OwnSymbolsOf S, F=S-firstChar, r=F.phi0, C=S-multiCat, sub=
SubTerms phi0, E=TheEqSymbOf S, R=RelSymbolsOf S; reconsider
TS=TermSymbolsOf S as non empty Subset of O by Th1; assume r<>E; then
not r in {E} by TARSKI:def 1; then not r in R\O by Th1; then
r in O or not r in R by XBOOLE_0:def 5; then
reconsider rr=r as Element of O by Def17;
C.sub is TS-valued by FOMODEL0:54; then
reconsider tail=C.sub as O-valued FinSequence;
phi0=<*rr*>^tail by Def38; hence thesis;
end;
