let p be Rational; :: thesis: ( ( numerator p = p or denominator p = 1 ) & 0 <= p implies p is Element of NAT )
assume that
A1: ( numerator p = p or denominator p = 1 ) and
A2: 0 <= p ; :: thesis: p is Element of NAT
p is Integer by A1, Th15;
hence p is Element of NAT by A2, INT_1:3; :: thesis: verum