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Definition df-rngisom 41659
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 ∈ V, 𝑠 ∈ V ↦ {𝑓 ∈ (𝑟 RngHomo 𝑠) ∣ 𝑓 ∈ (𝑠 RngHomo 𝑟)})
Distinct variable group:   𝑠,𝑟,𝑓

Detailed syntax breakdown of Definition df-rngisom
StepHypRef Expression
1 crngs 41657 . 2 class RngIsom
2 vr . . 3 setvar 𝑟
3 vs . . 3 setvar 𝑠
4 cvv 3172 . . 3 class V
5 vf . . . . . . 7 setvar 𝑓
65cv 1473 . . . . . 6 class 𝑓
76ccnv 5026 . . . . 5 class 𝑓
83cv 1473 . . . . . 6 class 𝑠
92cv 1473 . . . . . 6 class 𝑟
10 crngh 41656 . . . . . 6 class RngHomo
118, 9, 10co 6526 . . . . 5 class (𝑠 RngHomo 𝑟)
127, 11wcel 1976 . . . 4 wff 𝑓 ∈ (𝑠 RngHomo 𝑟)
139, 8, 10co 6526 . . . 4 class (𝑟 RngHomo 𝑠)
1412, 5, 13crab 2899 . . 3 class {𝑓 ∈ (𝑟 RngHomo 𝑠) ∣ 𝑓 ∈ (𝑠 RngHomo 𝑟)}
152, 3, 4, 4, 14cmpt2 6528 . 2 class (𝑟 ∈ V, 𝑠 ∈ V ↦ {𝑓 ∈ (𝑟 RngHomo 𝑠) ∣ 𝑓 ∈ (𝑠 RngHomo 𝑟)})
161, 15wceq 1474 1 wff RngIsom = (𝑟 ∈ V, 𝑠 ∈ V ↦ {𝑓 ∈ (𝑟 RngHomo 𝑠) ∣ 𝑓 ∈ (𝑠 RngHomo 𝑟)})
Colors of variables: wff setvar class
This definition is referenced by:  isrngisom  41667  rngimrcl  41668
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