Definition df-ric 20524

Description: Define the ring isomorphism relation, analogous to df-gic 19300: 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 20520	. 2 class ≃𝑟
2		crs 20519	. . . 4 class RingIso
3	2	ccnv 5646	. . 3 class ◡ RingIso
4		cvv 3454	. . . 4 class V
5		c1o 8430	. . . 4 class 1o
6	4, 5	cdif 3901	. . 3 class (V ∖ 1o)
7	3, 6	cima 5650	. 2 class (◡ RingIso “ (V ∖ 1o))
8	1, 7	wceq 1560	1 wff ≃𝑟 = (◡ RingIso “ (V ∖ 1o))

This definition is referenced by:  brric  20553