Definition df-ric 20347

Description: Define the ring isomorphism relation, analogous to df-gic 19126: 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 20343	. 2 class ≃𝑟
2		crs 20342	. . . 4 class RingIso
3	2	ccnv 5612	. . 3 class ◡ RingIso
4		cvv 3433	. . . 4 class V
5		c1o 8372	. . . 4 class 1o
6	4, 5	cdif 3896	. . 3 class (V ∖ 1o)
7	3, 6	cima 5616	. 2 class (◡ RingIso “ (V ∖ 1o))
8	1, 7	wceq 1540	1 wff ≃𝑟 = (◡ RingIso “ (V ∖ 1o))

This definition is referenced by:  brric  20373