Definition df-ric 20254

Description: Define the ring isomorphism relation, analogous to df-gic 19134: 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 20250	. 2 class ≃𝑟
2		crs 20249	. . . 4 class RingIso
3	2	ccnv 5676	. . 3 class ◡ RingIso
4		cvv 3475	. . . 4 class V
5		c1o 8459	. . . 4 class 1o
6	4, 5	cdif 3946	. . 3 class (V ∖ 1o)
7	3, 6	cima 5680	. 2 class (◡ RingIso “ (V ∖ 1o))
8	1, 7	wceq 1542	1 wff ≃𝑟 = (◡ RingIso “ (V ∖ 1o))

This definition is referenced by:  brric  20283