Definition df-ric 20657

Description: Define the ring isomorphism relation, analogous to df-gic 19390: 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 20615	. 2 class ≃𝑟
2		crs 20614	. . . 4 class RingIso
3	2	ccnv 5654	. . 3 class ◡ RingIso
4		cvv 3450	. . . 4 class V
5		c1o 8451	. . . 4 class 1o
6	4, 5	cdif 3896	. . 3 class (V ∖ 1o)
7	3, 6	cima 5658	. 2 class (◡ RingIso “ (V ∖ 1o))
8	1, 7	wceq 1570	1 wff ≃𝑟 = (◡ RingIso “ (V ∖ 1o))

This definition is used by:  ricrel  20658  brric  20659