let n, k, l be Element of NAT ; min* {n,k,l} = min (n,(min (k,l)))
A1:
min {n,k,l} = min* {n,k,l}
by Th1;
{n,k,l} = {n} \/ {k,l}
by ENUMSET1:2;
then A2:
min {n,k,l} = min ((min {n}),(min {k,l}))
by Th2;
min {k,l} = min (k,l)
by Th6;
hence
min* {n,k,l} = min (n,(min (k,l)))
by A2, A1, Th5; verum