Definition df-ric 19962

Description: Define the ring isomorphism relation, analogous to df-gic 18876: 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 19958	. 2 class ≃𝑟
2		crs 19957	. . . 4 class RingIso
3	2	ccnv 5588	. . 3 class ◡ RingIso
4		cvv 3432	. . . 4 class V
5		c1o 8290	. . . 4 class 1o
6	4, 5	cdif 3884	. . 3 class (V ∖ 1o)
7	3, 6	cima 5592	. 2 class (◡ RingIso “ (V ∖ 1o))
8	1, 7	wceq 1539	1 wff ≃𝑟 = (◡ RingIso “ (V ∖ 1o))

This definition is referenced by:  brric  19988