Definition df-ric 20423

Description: Define the ring isomorphism relation, analogous to df-gic 19201: Two (unital) rings are said to be isomorphic iff they are connected by at least one isomorphism. Isomorphic rings share all global ring properties, but to relate local properties requires knowledge of a specific isomorphism. (Contributed by AV, 24-Dec-2019.)

Assertion

Ref	Expression
df-ric	⊢ ≃𝑟 = (◡ RingIso “ (V ∖ 1o))

Detailed syntax breakdown of Definition df-ric

Step	Hyp	Ref	Expression
1		cric 20419	. 2 class ≃𝑟
2		crs 20418	. . . 4 class RingIso
3	2	ccnv 5631	. . 3 class ◡ RingIso
4		cvv 3442	. . . 4 class V
5		c1o 8400	. . . 4 class 1o
6	4, 5	cdif 3900	. . 3 class (V ∖ 1o)
7	3, 6	cima 5635	. 2 class (◡ RingIso “ (V ∖ 1o))
8	1, 7	wceq 1542	1 wff ≃𝑟 = (◡ RingIso “ (V ∖ 1o))

This definition is referenced by:  brric  20449