let M be Cardinal; :: thesis: for a being Aleph st ( a c= M or a in M ) holds
M is Aleph
let a be Aleph; :: thesis: ( ( a c= M or a in M ) implies M is Aleph )
assume ( a c= M or a in M ) ; :: thesis: M is Aleph
then A1: a c= M by ORDINAL1:16;
omega c= a by Th15;
then omega c= M by A1;
hence M is Aleph ; :: thesis: verum