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Definition df-fun 5806
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 14640). This is not the same as defining a specific function's mapping, which is typically done using the format of cmpt 4643 with the maps-to notation (see df-mpt 4645 and df-mpt2 6554). Contrast this predicate with the predicates to determine if some class is a function with a given domain (df-fn 5807), a function with a given domain and codomain (df-f 5808), a one-to-one function (df-f1 5809), an onto function (df-fo 5810), or a one-to-one onto function (df-f1o 5811). For alternate definitions, see dffun2 5814, dffun3 5815, dffun4 5816, dffun5 5817, dffun6 5819, dffun7 5830, dffun8 5831, and dffun9 5832. (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 5798 . 2 wff Fun 𝐴
31wrel 5043 . . 3 wff Rel 𝐴
41ccnv 5037 . . . . 5 class 𝐴
51, 4ccom 5042 . . . 4 class (𝐴𝐴)
6 cid 4948 . . . 4 class I
75, 6wss 3540 . . 3 wff (𝐴𝐴) ⊆ I
83, 7wa 383 . 2 wff (Rel 𝐴 ∧ (𝐴𝐴) ⊆ I )
92, 8wb 195 1 wff (Fun 𝐴 ↔ (Rel 𝐴 ∧ (𝐴𝐴) ⊆ I ))
Colors of variables: wff setvar class
This definition is referenced by:  dffun2  5814  funrel  5821  funss  5822  nffun  5826  funi  5834  funcocnv2  6074  dffv2  6181
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