Definition df-ric 20446

Description: Define the ring isomorphism relation, analogous to df-gic 19226: 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 20442	. 2 class ≃𝑟
2		crs 20441	. . . 4 class RingIso
3	2	ccnv 5617	. . 3 class ◡ RingIso
4		cvv 3431	. . . 4 class V
5		c1o 8388	. . . 4 class 1o
6	4, 5	cdif 3880	. . 3 class (V ∖ 1o)
7	3, 6	cima 5621	. 2 class (◡ RingIso “ (V ∖ 1o))
8	1, 7	wceq 1547	1 wff ≃𝑟 = (◡ RingIso “ (V ∖ 1o))

This definition is referenced by:  brric  20475