reserve p,p1,p2,q,r,F,G,G1,G2,H,H1,H2 for ZF-formula,
  x,x1,x2,y,y1,y2,z,z1,z2,s,t for Variable,
  a,X for set;

theorem
  Subformulae (F 'or' G) = Subformulae F \/ Subformulae G \/ {'not' G,
  'not' F, 'not' F '&' 'not' G, F 'or' G}
proof
  thus Subformulae (F 'or' G) = Subformulae ('not' F '&' 'not' G) \/ { F 'or'
  G } by ZF_LANG:82
    .= Subformulae 'not' F \/ Subformulae 'not' G \/ {'not' F '&' 'not' G}
  \/ {F 'or' G} by ZF_LANG:83
    .= Subformulae 'not' F \/ (Subformulae G \/ {'not' G}) \/ {'not' F '&'
  'not' G} \/ {F 'or' G} by ZF_LANG:82
    .= Subformulae F \/ {'not' F} \/ (Subformulae G \/ {'not' G}) \/ {'not'
  F '&' 'not' G} \/ {F 'or' G} by ZF_LANG:82
    .= Subformulae F \/ ((Subformulae G \/ {'not' G}) \/ {'not' F}) \/ {
  'not' F '&' 'not' G} \/ {F 'or' G} by XBOOLE_1:4
    .= Subformulae F \/ (Subformulae G \/ ({'not' G} \/ {'not' F})) \/ {
  'not' F '&' 'not' G} \/ {F 'or' G} by XBOOLE_1:4
    .= Subformulae F \/ (Subformulae G \/ {'not' G,'not' F}) \/ {'not' F '&'
  'not' G} \/ {F 'or' G} by ENUMSET1:1
    .= Subformulae F \/ Subformulae G \/ {'not' G,'not' F} \/ {'not' F '&'
  'not' G} \/ {F 'or' G} by XBOOLE_1:4
    .= Subformulae F \/ Subformulae G \/ {'not' G,'not' F} \/ ({'not' F '&'
  'not' G} \/ {F 'or' G}) by XBOOLE_1:4
    .= Subformulae F \/ Subformulae G \/ {'not' G,'not' F} \/ {'not' F '&'
  'not' G, F 'or' G} by ENUMSET1:1
    .= Subformulae F \/ Subformulae G \/ ({'not' G,'not' F} \/ {'not' F '&'
  'not' G, F 'or' G}) by XBOOLE_1:4
    .= Subformulae F \/ Subformulae G \/ {'not' G, 'not' F, 'not' F '&'
  'not' G, F 'or' G} by ENUMSET1:5;
end;
