Definition df-ric 20435

Description: Define the ring isomorphism relation, analogous to df-gic 19243: 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 20431	. 2 class ≃𝑟
2		crs 20430	. . . 4 class RingIso
3	2	ccnv 5653	. . 3 class ◡ RingIso
4		cvv 3459	. . . 4 class V
5		c1o 8473	. . . 4 class 1o
6	4, 5	cdif 3923	. . 3 class (V ∖ 1o)
7	3, 6	cima 5657	. 2 class (◡ RingIso “ (V ∖ 1o))
8	1, 7	wceq 1540	1 wff ≃𝑟 = (◡ RingIso “ (V ∖ 1o))

This definition is referenced by:  brric  20464