set IR = the InternalRel of R;
X c= the carrier of R by FINSUB_1:def 5;
then consider x being Element of R such that
A1: x in X and
A2: x is_minimal_wrt X, the InternalRel of R by B1, Th7;
take x ; :: thesis: ( x in X & x is_minimal_wrt X, the InternalRel of R )
thus ( x in X & x is_minimal_wrt X, the InternalRel of R ) by A1, A2; :: thesis: verum