Definition df-ric 19470

Description: Define the ring isomorphism relation, analogous to df-gic 18400: 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 19466	. 2 class ≃𝑟
2		crs 19465	. . . 4 class RingIso
3	2	ccnv 5554	. . 3 class ◡ RingIso
4		cvv 3494	. . . 4 class V
5		c1o 8095	. . . 4 class 1o
6	4, 5	cdif 3933	. . 3 class (V ∖ 1o)
7	3, 6	cima 5558	. 2 class (◡ RingIso “ (V ∖ 1o))
8	1, 7	wceq 1537	1 wff ≃𝑟 = (◡ RingIso “ (V ∖ 1o))

This definition is referenced by:  brric  19499