let x be RelStr ; :: according to PCS_0:def 4 :: thesis: ( x in rng (MSSet (P,Q)) implies x is transitive )
assume x in rng (MSSet (P,Q)) ; :: thesis: x is transitive
then x in {P,Q} by FUNCT_4:64;
hence x is transitive by TARSKI:def 2; :: thesis: verum