Definition df-ric 20455

Description: Define the ring isomorphism relation, analogous to df-gic 19235: 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 20451	. 2 class ≃𝑟
2		crs 20450	. . . 4 class RingIso
3	2	ccnv 5630	. . 3 class ◡ RingIso
4		cvv 3429	. . . 4 class V
5		c1o 8398	. . . 4 class 1o
6	4, 5	cdif 3886	. . 3 class (V ∖ 1o)
7	3, 6	cima 5634	. 2 class (◡ RingIso “ (V ∖ 1o))
8	1, 7	wceq 1542	1 wff ≃𝑟 = (◡ RingIso “ (V ∖ 1o))

This definition is referenced by:  brric  20481