let L be lower-bounded distributive algebraic LATTICE; :: thesis: ( ( for p being Element of L st p is pseudoprime holds
p is prime ) implies L is arithmetic )
assume for p being Element of L st p is pseudoprime holds
p is prime ; :: thesis: L is arithmetic
then L -waybelow is multiplicative by WAYBEL_7:46;
hence L is arithmetic by Th20; :: thesis: verum