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;
