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Definition df-fun 5791
Description: Define predicate that determines if some class 𝐴 is a function. Definition 10.1 of [Quine] p. 65. For example, the expression Fun cos is true once we define cosine (df-cos 14588). This is not the same as defining a specific function's mapping, which is typically done using the format of cmpt 4637 with the maps-to notation (see df-mpt 4639 and df-mpt2 6531). Contrast this predicate with the predicates to determine if some class is a function with a given domain (df-fn 5792), a function with a given domain and codomain (df-f 5793), a one-to-one function (df-f1 5794), an onto function (df-fo 5795), or a one-to-one onto function (df-f1o 5796). For alternate definitions, see dffun2 5799, dffun3 5800, dffun4 5801, dffun5 5802, dffun6 5804, dffun7 5815, dffun8 5816, and dffun9 5817. (Contributed by NM, 1-Aug-1994.)
Assertion
Ref Expression
df-fun (Fun 𝐴 ↔ (Rel 𝐴 ∧ (𝐴𝐴) ⊆ I ))

Detailed syntax breakdown of Definition df-fun
StepHypRef Expression
1 cA . . 3 class 𝐴
21wfun 5783 . 2 wff Fun 𝐴
31wrel 5032 . . 3 wff Rel 𝐴
41ccnv 5026 . . . . 5 class 𝐴
51, 4ccom 5031 . . . 4 class (𝐴𝐴)
6 cid 4937 . . . 4 class I
75, 6wss 3539 . . 3 wff (𝐴𝐴) ⊆ I
83, 7wa 382 . 2 wff (Rel 𝐴 ∧ (𝐴𝐴) ⊆ I )
92, 8wb 194 1 wff (Fun 𝐴 ↔ (Rel 𝐴 ∧ (𝐴𝐴) ⊆ I ))
Colors of variables: wff setvar class
This definition is referenced by:  dffun2  5799  funrel  5806  funss  5807  nffun  5811  funi  5819  funcocnv2  6058  dffv2  6165
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