theorem Th24:
  J,v |= p => q iff (J,v |= p implies J,v |= q)
proof
  thus J,v |= p => q & J,v |= p implies J,v |= q by Th23;
  assume J,v |= p implies J,v |= q;
  then Valid(p, J).v = TRUE implies Valid(q, J).v = TRUE;
  then Valid(p, J).v = FALSE or Valid(q, J).v = TRUE by XBOOLEAN:def 3;
  hence thesis by Th23;
end;
