Definition df-ric 19466

Description: Define the ring isomorphism relation, analogous to df-gic 18392: 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 19462	. 2 class ≃𝑟
2		crs 19461	. . . 4 class RingIso
3	2	ccnv 5518	. . 3 class ◡ RingIso
4		cvv 3441	. . . 4 class V
5		c1o 8078	. . . 4 class 1o
6	4, 5	cdif 3878	. . 3 class (V ∖ 1o)
7	3, 6	cima 5522	. 2 class (◡ RingIso “ (V ∖ 1o))
8	1, 7	wceq 1538	1 wff ≃𝑟 = (◡ RingIso “ (V ∖ 1o))

This definition is referenced by:  brric  19492