Definition df-ric 20755

Description: Define the ring isomorphism relation, analogous to df-gic 19486: 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 19486. (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 20713	. 2 class ≃𝑟
2		crs 20712	. . . 4 class RingIso
3	2	ccnv 5653	. . 3 class ◡ RingIso
4		cvv 3453	. . . 4 class V
5		c1o 8480	. . . 4 class 1o
6	4, 5	cdif 4047	. . 3 class (V ∖ 1o)
7	3, 6	cima 5657	. 2 class (◡ RingIso “ (V ∖ 1o))
8	1, 7	wceq 1569	1 wff ≃𝑟 = (◡ RingIso “ (V ∖ 1o))

This definition is used by:  ricrel  20756  brric  20757