Metamath Proof Explorer


Definition df-dvr

Description: Define ring division. (Contributed by Mario Carneiro, 2-Jul-2014)

Ref Expression
Assertion df-dvr /r=rVxBaser,yUnitrxrinvrry

Detailed syntax breakdown

Step Hyp Ref Expression
0 cdvr class/r
1 vr setvarr
2 cvv classV
3 vx setvarx
4 cbs classBase
5 1 cv setvarr
6 5 4 cfv classBaser
7 vy setvary
8 cui classUnit
9 5 8 cfv classUnitr
10 3 cv setvarx
11 cmulr class𝑟
12 5 11 cfv classr
13 cinvr classinvr
14 5 13 cfv classinvrr
15 7 cv setvary
16 15 14 cfv classinvrry
17 10 16 12 co classxrinvrry
18 3 7 6 9 17 cmpo classxBaser,yUnitrxrinvrry
19 1 2 18 cmpt classrVxBaser,yUnitrxrinvrry
20 0 19 wceq wff/r=rVxBaser,yUnitrxrinvrry