Definition df-rngisom 41888

Description: Define the set of non-unital ring isomorphisms from r to s. (Contributed by AV, 20-Feb-2020.)

Assertion

Ref	Expression
df-rngisom	|- RngIsom = ( r e. _V , s e. _V |-> { f e. ( r RngHomo s ) | `' f e. ( s RngHomo r ) } )

Distinct variable group:   s, r, f

Detailed syntax breakdown of Definition df-rngisom

Step	Hyp	Ref	Expression
1		crngs 41886	. 2 class RngIsom
2		vr	. . 3 setvar r
3		vs	. . 3 setvar s
4		cvv 3200	. . 3 class _V
5		vf	. . . . . . 7 setvar f
6	5	cv 1482	. . . . . 6 class f
7	6	ccnv 5113	. . . . 5 class `' f
8	3	cv 1482	. . . . . 6 class s
9	2	cv 1482	. . . . . 6 class r
10		crngh 41885	. . . . . 6 class RngHomo
11	8, 9, 10	co 6650	. . . . 5 class ( s RngHomo r )
12	7, 11	wcel 1990	. . . 4 wff `' f e. ( s RngHomo r )
13	9, 8, 10	co 6650	. . . 4 class ( r RngHomo s )
14	12, 5, 13	crab 2916	. . 3 class { f e. ( r RngHomo s ) | `' f e. ( s RngHomo r ) }
15	2, 3, 4, 4, 14	cmpt2 6652	. 2 class ( r e. _V , s e. _V |-> { f e. ( r RngHomo s ) | `' f e. ( s RngHomo r ) } )
16	1, 15	wceq 1483	1 wff RngIsom = ( r e. _V , s e. _V |-> { f e. ( r RngHomo s ) | `' f e. ( s RngHomo r ) } )

This definition is referenced by:  isrngisom  41896  rngimrcl  41897