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Definition df-dfat 43718
 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 43715 . 2 wff 𝐹 defAt 𝐴
42cdm 5520 . . . 4 class dom 𝐹
51, 4wcel 2111 . . 3 wff 𝐴 ∈ dom 𝐹
61csn 4525 . . . . 5 class {𝐴}
72, 6cres 5522 . . . 4 class (𝐹 ↾ {𝐴})
87wfun 6319 . . 3 wff Fun (𝐹 ↾ {𝐴})
95, 8wa 399 . 2 wff (𝐴 ∈ dom 𝐹 ∧ Fun (𝐹 ↾ {𝐴}))
103, 9wb 209 1 wff (𝐹 defAt 𝐴 ↔ (𝐴 ∈ dom 𝐹 ∧ Fun (𝐹 ↾ {𝐴})))
 Colors of variables: wff setvar class This definition is referenced by:  dfateq12d  43725  nfdfat  43726  dfdfat2  43727  fundmdfat  43728  dfatprc  43729  dfatelrn  43730  ndmafv  43739  nfunsnafv  43741  afvpcfv0  43745  afvfvn0fveq  43749  afv0nbfvbi  43750  fnbrafvb  43753  afvelrn  43767  afvres  43771  tz6.12-afv  43772  dmfcoafv  43774  afvco2  43775  aovmpt4g  43800  ndmafv2nrn  43821  funressndmafv2rn  43822  nfunsnafv2  43824  dmafv2rnb  43828  afv2res  43838  tz6.12-afv2  43839  dfatbrafv2b  43844  dfatdmfcoafv2  43853  dfatcolem  43854  dfatco  43855  afv2ndeffv0  43859  afv2fvn0fveq  43863
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