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Definition df-dfat 40965
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 40962 . 2 wff 𝐹 defAt 𝐴
42cdm 5112 . . . 4 class dom 𝐹
51, 4wcel 1989 . . 3 wff 𝐴 ∈ dom 𝐹
61csn 4175 . . . . 5 class {𝐴}
72, 6cres 5114 . . . 4 class (𝐹 ↾ {𝐴})
87wfun 5880 . . 3 wff Fun (𝐹 ↾ {𝐴})
95, 8wa 384 . 2 wff (𝐴 ∈ dom 𝐹 ∧ Fun (𝐹 ↾ {𝐴}))
103, 9wb 196 1 wff (𝐹 defAt 𝐴 ↔ (𝐴 ∈ dom 𝐹 ∧ Fun (𝐹 ↾ {𝐴})))
Colors of variables: wff setvar class
This definition is referenced by:  dfateq12d  40978  nfdfat  40979  dfdfat2  40980  ndmafv  40989  nfunsnafv  40991  afvpcfv0  40995  afvfvn0fveq  40999  afv0nbfvbi  41000  fnbrafvb  41003  afvelrn  41017  afvres  41021  tz6.12-afv  41022  dmfcoafv  41024  afvco2  41025  aovmpt4g  41050
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