Definition df-ric 20475

Description: Define the ring isomorphism relation, analogous to df-gic 19278: 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 20471	. 2 class ≃𝑟
2		crs 20470	. . . 4 class RingIso
3	2	ccnv 5684	. . 3 class ◡ RingIso
4		cvv 3480	. . . 4 class V
5		c1o 8499	. . . 4 class 1o
6	4, 5	cdif 3948	. . 3 class (V ∖ 1o)
7	3, 6	cima 5688	. 2 class (◡ RingIso “ (V ∖ 1o))
8	1, 7	wceq 1540	1 wff ≃𝑟 = (◡ RingIso “ (V ∖ 1o))

This definition is referenced by:  brric  20504