Definition df-ric 20411

Description: Define the ring isomorphism relation, analogous to df-gic 19189: 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 20407	. 2 class ≃𝑟
2		crs 20406	. . . 4 class RingIso
3	2	ccnv 5623	. . 3 class ◡ RingIso
4		cvv 3440	. . . 4 class V
5		c1o 8390	. . . 4 class 1o
6	4, 5	cdif 3898	. . 3 class (V ∖ 1o)
7	3, 6	cima 5627	. 2 class (◡ RingIso “ (V ∖ 1o))
8	1, 7	wceq 1541	1 wff ≃𝑟 = (◡ RingIso “ (V ∖ 1o))

This definition is referenced by:  brric  20437