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Definition df-fun 6043
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 14992). This is not the same as defining a specific function's mapping, which is typically done using the format of cmpt 4873 with the maps-to notation (see df-mpt 4874 and df-mpt2 6810). Contrast this predicate with the predicates to determine if some class is a function with a given domain (df-fn 6044), a function with a given domain and codomain (df-f 6045), a one-to-one function (df-f1 6046), an onto function (df-fo 6047), or a one-to-one onto function (df-f1o 6048). For alternate definitions, see dffun2 6051, dffun3 6052, dffun4 6053, dffun5 6054, dffun6 6056, dffun7 6068, dffun8 6069, and dffun9 6070. (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 6035 . 2 wff Fun 𝐴
31wrel 5263 . . 3 wff Rel 𝐴
41ccnv 5257 . . . . 5 class 𝐴
51, 4ccom 5262 . . . 4 class (𝐴𝐴)
6 cid 5165 . . . 4 class I
75, 6wss 3707 . . 3 wff (𝐴𝐴) ⊆ I
83, 7wa 383 . 2 wff (Rel 𝐴 ∧ (𝐴𝐴) ⊆ I )
92, 8wb 196 1 wff (Fun 𝐴 ↔ (Rel 𝐴 ∧ (𝐴𝐴) ⊆ I ))
Colors of variables: wff setvar class
This definition is referenced by:  dffun2  6051  funrel  6058  funss  6060  nffun  6064  funi  6073  funcocnv2  6314  dffv2  6425
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