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Definition df-lmim 19795
 Description: An isomorphism of modules is a homomorphism which is also a bijection, i.e. it preserves equality as well as the group and scalar operations. (Contributed by Stefan O'Rear, 21-Jan-2015.)
Assertion
Ref Expression
df-lmim LMIso = (𝑠 ∈ LMod, 𝑡 ∈ LMod ↦ {𝑔 ∈ (𝑠 LMHom 𝑡) ∣ 𝑔:(Base‘𝑠)–1-1-onto→(Base‘𝑡)})
Distinct variable group:   𝑡,𝑠,𝑔

Detailed syntax breakdown of Definition df-lmim
StepHypRef Expression
1 clmim 19792 . 2 class LMIso
2 vs . . 3 setvar 𝑠
3 vt . . 3 setvar 𝑡
4 clmod 19634 . . 3 class LMod
52cv 1537 . . . . . 6 class 𝑠
6 cbs 16483 . . . . . 6 class Base
75, 6cfv 6343 . . . . 5 class (Base‘𝑠)
83cv 1537 . . . . . 6 class 𝑡
98, 6cfv 6343 . . . . 5 class (Base‘𝑡)
10 vg . . . . . 6 setvar 𝑔
1110cv 1537 . . . . 5 class 𝑔
127, 9, 11wf1o 6342 . . . 4 wff 𝑔:(Base‘𝑠)–1-1-onto→(Base‘𝑡)
13 clmhm 19791 . . . . 5 class LMHom
145, 8, 13co 7149 . . . 4 class (𝑠 LMHom 𝑡)
1512, 10, 14crab 3137 . . 3 class {𝑔 ∈ (𝑠 LMHom 𝑡) ∣ 𝑔:(Base‘𝑠)–1-1-onto→(Base‘𝑡)}
162, 3, 4, 4, 15cmpo 7151 . 2 class (𝑠 ∈ LMod, 𝑡 ∈ LMod ↦ {𝑔 ∈ (𝑠 LMHom 𝑡) ∣ 𝑔:(Base‘𝑠)–1-1-onto→(Base‘𝑡)})
171, 16wceq 1538 1 wff LMIso = (𝑠 ∈ LMod, 𝑡 ∈ LMod ↦ {𝑔 ∈ (𝑠 LMHom 𝑡) ∣ 𝑔:(Base‘𝑠)–1-1-onto→(Base‘𝑡)})
 Colors of variables: wff setvar class This definition is referenced by:  lmimfn  19798  islmim  19834
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