theorem Th29:
  J,v |= All(x,p) iff for w st for y st x<>y holds w.y = v.y holds J,w |= p
proof
A1: now
    assume
A2: for w st for y st x<>y holds w.y = v.y holds J,w |= p;
    for w st for y st x<>y holds w.y = v.y holds Valid(p,J).w = TRUE
    by A2,Def7;
    hence J,v |= All(x,p) by Th20;
  end;
  J,v |= All(x,p) implies for w st for y st x<>y holds w.y = v.y holds J,w |= p
  by Th20;
  hence thesis by A1;
end;
