Definition df-ric 20557

Description: Define the ring isomorphism relation, analogous to df-gic 19330: 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 20553	. 2 class ≃𝑟
2		crs 20552	. . . 4 class RingIso
3	2	ccnv 5661	. . 3 class ◡ RingIso
4		cvv 3463	. . . 4 class V
5		c1o 8446	. . . 4 class 1o
6	4, 5	cdif 3910	. . 3 class (V ∖ 1o)
7	3, 6	cima 5665	. 2 class (◡ RingIso “ (V ∖ 1o))
8	1, 7	wceq 1567	1 wff ≃𝑟 = (◡ RingIso “ (V ∖ 1o))

This definition is referenced by:  brric  20586