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Definition df-fun 6327
 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 15419). This is not the same as defining a specific function's mapping, which is typically done using the format of cmpt 5111 with the maps-to notation (see df-mpt 5112 and df-mpo 7141). Contrast this predicate with the predicates to determine if some class is a function with a given domain (df-fn 6328), a function with a given domain and codomain (df-f 6329), a one-to-one function (df-f1 6330), an onto function (df-fo 6331), or a one-to-one onto function (df-f1o 6332). For alternate definitions, see dffun2 6335, dffun3 6336, dffun4 6337, dffun5 6338, dffun6 6340, dffun7 6352, dffun8 6353, and dffun9 6354. (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 6319 . 2 wff Fun 𝐴
31wrel 5525 . . 3 wff Rel 𝐴
41ccnv 5519 . . . . 5 class 𝐴
51, 4ccom 5524 . . . 4 class (𝐴𝐴)
6 cid 5425 . . . 4 class I
75, 6wss 3881 . . 3 wff (𝐴𝐴) ⊆ I
83, 7wa 399 . 2 wff (Rel 𝐴 ∧ (𝐴𝐴) ⊆ I )
92, 8wb 209 1 wff (Fun 𝐴 ↔ (Rel 𝐴 ∧ (𝐴𝐴) ⊆ I ))
 Colors of variables: wff setvar class This definition is referenced by:  dffun2  6335  funrel  6342  funss  6344  nffun  6348  funi  6357  funcocnv2  6615  dffv2  6734  funALTVfun  36110
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