Definition df-ric 20449

Description: Define the ring isomorphism relation, analogous to df-gic 19229: 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 20445	. 2 class ≃𝑟
2		crs 20444	. . . 4 class RingIso
3	2	ccnv 5619	. . 3 class ◡ RingIso
4		cvv 3433	. . . 4 class V
5		c1o 8392	. . . 4 class 1o
6	4, 5	cdif 3881	. . 3 class (V ∖ 1o)
7	3, 6	cima 5623	. 2 class (◡ RingIso “ (V ∖ 1o))
8	1, 7	wceq 1548	1 wff ≃𝑟 = (◡ RingIso “ (V ∖ 1o))

This definition is referenced by:  brric  20478