Definition df-ric 20591

Description: Define the ring isomorphism relation, analogous to df-gic 19325: 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 20549	. 2 class ≃𝑟
2		crs 20548	. . . 4 class RingIso
3	2	ccnv 5660	. . 3 class ◡ RingIso
4		cvv 3455	. . . 4 class V
5		c1o 8442	. . . 4 class 1o
6	4, 5	cdif 3902	. . 3 class (V ∖ 1o)
7	3, 6	cima 5664	. 2 class (◡ RingIso “ (V ∖ 1o))
8	1, 7	wceq 1570	1 wff ≃𝑟 = (◡ RingIso “ (V ∖ 1o))

This definition is referenced by:  ricrel  20592  brric  20593