Definition df-ric 20391

Description: Define the ring isomorphism relation, analogous to df-gic 19199: 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 20387	. 2 class ≃𝑟
2		crs 20386	. . . 4 class RingIso
3	2	ccnv 5640	. . 3 class ◡ RingIso
4		cvv 3450	. . . 4 class V
5		c1o 8430	. . . 4 class 1o
6	4, 5	cdif 3914	. . 3 class (V ∖ 1o)
7	3, 6	cima 5644	. 2 class (◡ RingIso “ (V ∖ 1o))
8	1, 7	wceq 1540	1 wff ≃𝑟 = (◡ RingIso “ (V ∖ 1o))

This definition is referenced by:  brric  20420