Definition df-ric 20501

Description: Define the ring isomorphism relation, analogous to df-gic 19300: 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 20497	. 2 class ≃𝑟
2		crs 20496	. . . 4 class RingIso
3	2	ccnv 5699	. . 3 class ◡ RingIso
4		cvv 3488	. . . 4 class V
5		c1o 8515	. . . 4 class 1o
6	4, 5	cdif 3973	. . 3 class (V ∖ 1o)
7	3, 6	cima 5703	. 2 class (◡ RingIso “ (V ∖ 1o))
8	1, 7	wceq 1537	1 wff ≃𝑟 = (◡ RingIso “ (V ∖ 1o))

This definition is referenced by:  brric  20530