let UN be Universe; :: thesis: for b being Object of (RingCat UN)
for b9 being Element of RingObjects UN st b = b9 holds
id b = ID b9
set C = RingCat UN;
set V = RingObjects UN;
let b be Object of (RingCat UN); :: thesis: for b9 being Element of RingObjects UN st b = b9 holds
id b = ID b9
let b9 be Element of RingObjects UN; :: thesis: ( b = b9 implies id b = ID b9 )
assume b = b9 ; :: thesis: id b = ID b9
hence id b = (ID (RingObjects UN)) . b9 by CAT_1:def 5
.= ID b9 by Def22 ;
:: thesis: verum