Definition df-ric 20409

Description: Define the ring isomorphism relation, analogous to df-gic 19187: 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 20405	. 2 class ≃𝑟
2		crs 20404	. . . 4 class RingIso
3	2	ccnv 5621	. . 3 class ◡ RingIso
4		cvv 3438	. . . 4 class V
5		c1o 8388	. . . 4 class 1o
6	4, 5	cdif 3896	. . 3 class (V ∖ 1o)
7	3, 6	cima 5625	. 2 class (◡ RingIso “ (V ∖ 1o))
8	1, 7	wceq 1541	1 wff ≃𝑟 = (◡ RingIso “ (V ∖ 1o))

This definition is referenced by:  brric  20435