Definition df-ric 18718

Description: Define the ring isomorphism relation, analogous to df-gic 17702: 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 18714	. 2 class ≃𝑟
2		crs 18713	. . . 4 class RingIso
3	2	ccnv 5113	. . 3 class ◡ RingIso
4		cvv 3200	. . . 4 class V
5		c1o 7553	. . . 4 class 1𝑜
6	4, 5	cdif 3571	. . 3 class (V ∖ 1𝑜)
7	3, 6	cima 5117	. 2 class (◡ RingIso “ (V ∖ 1𝑜))
8	1, 7	wceq 1483	1 wff ≃𝑟 = (◡ RingIso “ (V ∖ 1𝑜))

This definition is referenced by:  brric  18744