Definition df-ric 20253

Description: Define the ring isomorphism relation, analogous to df-gic 19133: 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 20249	. 2 class ≃𝑟
2		crs 20248	. . . 4 class RingIso
3	2	ccnv 5675	. . 3 class ◡ RingIso
4		cvv 3474	. . . 4 class V
5		c1o 8458	. . . 4 class 1o
6	4, 5	cdif 3945	. . 3 class (V ∖ 1o)
7	3, 6	cima 5679	. 2 class (◡ RingIso “ (V ∖ 1o))
8	1, 7	wceq 1541	1 wff ≃𝑟 = (◡ RingIso “ (V ∖ 1o))

This definition is referenced by:  brric  20282