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

per cases then ( ( 2 <= p & p < 3 ) or ( 3 <= p & p <= 3 + 1 ) ) by NAT_1:13;

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

hence ( p = 2 or p = 3 ) by Th1; :: thesis: verum

end;

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

hence ( p = 2 or p = 3 ) by XPRIMES0:4, NAT_1:9; :: thesis: verum

end;

end;