theorem Th95:
  x in vf C
  proof
    card Coim(C,[x,s]) = 1 by CONTEXT;
    then consider a such that
A1: Coim(C,[x,s]) = {a} by CARD_2:42;
    a in {a} by TARSKI:def 1;
    then a in dom C & C.a in {[x,s]} by A1,FUNCT_1:def 7;
    then
A2: [x,s] = C.a in rng C by TARSKI:def 1,FUNCT_1:def 3;
    [x,s] in [:Union X, the carrier of S:] by ZFMISC_1:87;
    then [x,s] in rng C /\ [:Union X, the carrier of S:] by A2,XBOOLE_0:def 4;
    hence thesis by XTUPLE_0:def 12;
  end;
