Definition df-ric 20643

Description: Define the ring isomorphism relation, analogous to df-gic 19376: 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 20601	. 2 class ≃𝑟
2		crs 20600	. . . 4 class RingIso
3	2	ccnv 5662	. . 3 class ◡ RingIso
4		cvv 3457	. . . 4 class V
5		c1o 8452	. . . 4 class 1o
6	4, 5	cdif 3903	. . 3 class (V ∖ 1o)
7	3, 6	cima 5666	. 2 class (◡ RingIso “ (V ∖ 1o))
8	1, 7	wceq 1570	1 wff ≃𝑟 = (◡ RingIso “ (V ∖ 1o))

This definition is used by:  ricrel  20644  brric  20645