let p be Prime; :: thesis: ( not p < 7 or p = 2 or p = 3 or p = 5 )
assume p < 7 ; :: thesis: ( p = 2 or p = 3 or p = 5 )
then ( 1 + 1 < p + 1 & p < 6 + 1 ) by XREAL_1:6, INT_2:def 4;

per cases then ( ( 2 <= p & p < 5 ) or ( 5 <= p & p <= 5 + 1 ) ) by NAT_1:13;

suppose ( 2 <= p & p < 5 ) ; :: thesis: ( p = 2 or p = 3 or p = 5 )

hence ( p = 2 or p = 3 or p = 5 ) by Ttool5a; :: thesis: verum

end;

suppose ( 5 <= p & p <= 5 + 1 ) ; :: thesis: ( p = 2 or p = 3 or p = 5 )

then p = 5 by XPRIMES0:6, NAT_1:9;
hence ( p = 2 or p = 3 or p = 5 ) ; :: thesis: verum

end;

end;