Definition df-ric 20492

Description: Define the ring isomorphism relation, analogous to df-gic 19291: 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 20488	. 2 class ≃𝑟
2		crs 20487	. . . 4 class RingIso
3	2	ccnv 5688	. . 3 class ◡ RingIso
4		cvv 3478	. . . 4 class V
5		c1o 8498	. . . 4 class 1o
6	4, 5	cdif 3960	. . 3 class (V ∖ 1o)
7	3, 6	cima 5692	. 2 class (◡ RingIso “ (V ∖ 1o))
8	1, 7	wceq 1537	1 wff ≃𝑟 = (◡ RingIso “ (V ∖ 1o))

This definition is referenced by:  brric  20521