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Definition df-dfat 43195
Description: Definition of the predicate that determines if some class 𝐹 is defined as function for an argument 𝐴 or, in other words, if the function value for some class 𝐹 for an argument 𝐴 is defined. We say that 𝐹 is defined at 𝐴 if a 𝐹 is a function restricted to the member 𝐴 of its domain. (Contributed by Alexander van der Vekens, 25-May-2017.)
Assertion
Ref Expression
df-dfat (𝐹 defAt 𝐴 ↔ (𝐴 ∈ dom 𝐹 ∧ Fun (𝐹 ↾ {𝐴})))

Detailed syntax breakdown of Definition df-dfat
StepHypRef Expression
1 cA . . 3 class 𝐴
2 cF . . 3 class 𝐹
31, 2wdfat 43192 . 2 wff 𝐹 defAt 𝐴
42cdm 5548 . . . 4 class dom 𝐹
51, 4wcel 2105 . . 3 wff 𝐴 ∈ dom 𝐹
61csn 4557 . . . . 5 class {𝐴}
72, 6cres 5550 . . . 4 class (𝐹 ↾ {𝐴})
87wfun 6342 . . 3 wff Fun (𝐹 ↾ {𝐴})
95, 8wa 396 . 2 wff (𝐴 ∈ dom 𝐹 ∧ Fun (𝐹 ↾ {𝐴}))
103, 9wb 207 1 wff (𝐹 defAt 𝐴 ↔ (𝐴 ∈ dom 𝐹 ∧ Fun (𝐹 ↾ {𝐴})))
Colors of variables: wff setvar class
This definition is referenced by:  dfateq12d  43202  nfdfat  43203  dfdfat2  43204  fundmdfat  43205  dfatprc  43206  dfatelrn  43207  ndmafv  43216  nfunsnafv  43218  afvpcfv0  43222  afvfvn0fveq  43226  afv0nbfvbi  43227  fnbrafvb  43230  afvelrn  43244  afvres  43248  tz6.12-afv  43249  dmfcoafv  43251  afvco2  43252  aovmpt4g  43277  ndmafv2nrn  43298  funressndmafv2rn  43299  nfunsnafv2  43301  dmafv2rnb  43305  afv2res  43315  tz6.12-afv2  43316  dfatbrafv2b  43321  dfatdmfcoafv2  43330  dfatcolem  43331  dfatco  43332  afv2ndeffv0  43336  afv2fvn0fveq  43340
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