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 A1: ( a c= M or a in M ) ; :: thesis: M is Aleph
omega c= a by Th25;
then omega c= M by A1, XBOOLE_1:1;
hence M is Aleph ; :: thesis: verum