Definition df-ric 19877

Description: Define the ring isomorphism relation, analogous to df-gic 18791: 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 19873	. 2 class ≃𝑟
2		crs 19872	. . . 4 class RingIso
3	2	ccnv 5579	. . 3 class ◡ RingIso
4		cvv 3422	. . . 4 class V
5		c1o 8260	. . . 4 class 1o
6	4, 5	cdif 3880	. . 3 class (V ∖ 1o)
7	3, 6	cima 5583	. 2 class (◡ RingIso “ (V ∖ 1o))
8	1, 7	wceq 1539	1 wff ≃𝑟 = (◡ RingIso “ (V ∖ 1o))

This definition is referenced by:  brric  19903