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 5624	. . 3 class ◡ RingIso
4		cvv 3430	. . . 4 class V
5		c1o 8392	. . . 4 class 1o
6	4, 5	cdif 3887	. . 3 class (V ∖ 1o)
7	3, 6	cima 5628	. 2 class (◡ RingIso “ (V ∖ 1o))
8	1, 7	wceq 1542	1 wff ≃𝑟 = (◡ RingIso “ (V ∖ 1o))

This definition is referenced by:  brric  20475