Definition df-ric 20384

Description: Define the ring isomorphism relation, analogous to df-gic 19192: 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 20380	. 2 class ≃𝑟
2		crs 20379	. . . 4 class RingIso
3	2	ccnv 5637	. . 3 class ◡ RingIso
4		cvv 3447	. . . 4 class V
5		c1o 8427	. . . 4 class 1o
6	4, 5	cdif 3911	. . 3 class (V ∖ 1o)
7	3, 6	cima 5641	. 2 class (◡ RingIso “ (V ∖ 1o))
8	1, 7	wceq 1540	1 wff ≃𝑟 = (◡ RingIso “ (V ∖ 1o))

This definition is referenced by:  brric  20413