Definition df-ric 20393

Description: Define the ring isomorphism relation, analogous to df-gic 19172: 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 20389	. 2 class ≃𝑟
2		crs 20388	. . . 4 class RingIso
3	2	ccnv 5613	. . 3 class ◡ RingIso
4		cvv 3436	. . . 4 class V
5		c1o 8378	. . . 4 class 1o
6	4, 5	cdif 3894	. . 3 class (V ∖ 1o)
7	3, 6	cima 5617	. 2 class (◡ RingIso “ (V ∖ 1o))
8	1, 7	wceq 1541	1 wff ≃𝑟 = (◡ RingIso “ (V ∖ 1o))

This definition is referenced by:  brric  20419