consider m1, n1 being Integer such that
n1 > 0 and
A11: p = m1 / n1 by Th2;
consider m2, n2 being Integer such that
n2 > 0 and
A12: q = m2 / n2 by Th2;
p / q = p * (1 / (m2 / n2)) by A12
.= p * ((1 * n2) / m2) by XCMPLX_1:77
.= (m1 * n2) / (n1 * m2) by A11, XCMPLX_1:76 ;
hence p / q is rational by Th3; :: thesis: verum