let a, b be natural Ordinal; :: thesis: ( [a,b] in RATplus implies ( a,b are_relative_prime & b <> {} ) )
assume
[a,b] in RATplus
; :: thesis: ( a,b are_relative_prime & b <> {} )
then consider c, d being Element of omega such that
A1:
( [a,b] = [c,d] & c,d are_relative_prime & d <> {} )
;
( a = c & b = d )
by A1, ZFMISC_1:33;
hence
( a,b are_relative_prime & b <> {} )
by A1; :: thesis: verum