Definition df-ric 18541

Description: Define the ring isomorphism relation, analogous to df-gic 17525: 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 18537	. 2 class ≃𝑟
2		crs 18536	. . . 4 class RingIso
3	2	ccnv 5037	. . 3 class ◡ RingIso
4		cvv 3173	. . . 4 class V
5		c1o 7440	. . . 4 class 1𝑜
6	4, 5	cdif 3537	. . 3 class (V ∖ 1𝑜)
7	3, 6	cima 5041	. 2 class (◡ RingIso “ (V ∖ 1𝑜))
8	1, 7	wceq 1475	1 wff ≃𝑟 = (◡ RingIso “ (V ∖ 1𝑜))

This definition is referenced by:  brric  18567