A3: R is_reflexive_in field R by Def9;
A4: P is_reflexive_in field P by Def9;

now :: thesis: for a being set st a in field (P /\ R) holds
[a,a] in P /\ R

let a be set ; :: thesis: ( a in field (P /\ R) implies [a,a] in P /\ R )
assume A7: a in field (P /\ R) ; :: thesis: [a,a] in P /\ R
A8: field (P /\ R) c= (field P) /\ (field R) by RELAT_1:19;
then a in field R by A7, XBOOLE_0:def 4;
then A9: [a,a] in R by A3, Def1;
a in field P by A8, A7, XBOOLE_0:def 4;
then [a,a] in P by A4, Def1;
hence [a,a] in P /\ R by A9, XBOOLE_0:def 4; :: thesis: verum

end;

hence P /\ R is reflexive by Def1, Def9; :: thesis: verum