Definition df-ric 20743

Description: Define the ring isomorphism relation, analogous to df-gic 19474: 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 Jeff Madsen, 16-Jun-2011.) Adapted to df-gic 19474. (Revised 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 20701	. 2 class ≃𝑟
2		crs 20700	. . . 4 class RingIso
3	2	ccnv 5650	. . 3 class ◡ RingIso
4		cvv 3451	. . . 4 class V
5		c1o 8469	. . . 4 class 1o
6	4, 5	cdif 3896	. . 3 class (V ∖ 1o)
7	3, 6	cima 5654	. 2 class (◡ RingIso “ (V ∖ 1o))
8	1, 7	wceq 1570	1 wff ≃𝑟 = (◡ RingIso “ (V ∖ 1o))

This definition is used by:  ricrel  20744  brric  20745