Definition df-ric 20360

Description: Define the ring isomorphism relation, analogous to df-gic 19168: 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 20356	. 2 class ≃𝑟
2		crs 20355	. . . 4 class RingIso
3	2	ccnv 5630	. . 3 class ◡ RingIso
4		cvv 3444	. . . 4 class V
5		c1o 8404	. . . 4 class 1o
6	4, 5	cdif 3908	. . 3 class (V ∖ 1o)
7	3, 6	cima 5634	. 2 class (◡ RingIso “ (V ∖ 1o))
8	1, 7	wceq 1540	1 wff ≃𝑟 = (◡ RingIso “ (V ∖ 1o))

This definition is referenced by:  brric  20389