let UN be Universe; :: thesis: for b being Object of
for b' being Element of GroupObjects UN st b = b' holds
id b = ID b'
set C = GroupCat UN;
set V = GroupObjects UN;
let b be Object of ; :: thesis: for b' being Element of GroupObjects UN st b = b' holds
id b = ID b'
let b' be Element of GroupObjects UN; :: thesis: ( b = b' implies id b = ID b' )
assume b = b' ; :: thesis: id b = ID b'
hence id b = (ID (GroupObjects UN)) . b' by CAT_1:def 5
.= ID b' by Def34 ;
:: thesis: verum