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Definition df-fun 5440
Description: Define predicate that determines if some class is a function. Definition 10.1 of [Quine] p. 65. For example, the expression is true once we define cosine (df-cos 13203). This is not the same as defining a specific function's mapping, which is typically done using the format of cmpt 4376 with the maps-to notation (see df-mpt 4378 and df-mpt2 6108). Contrast this predicate with the predicates to determine if some class is a function with a given domain (df-fn 5441), a function with a given domain and codomain (df-f 5442), a one-to-one function (df-f1 5443), an onto function (df-fo 5444), or a one-to-one onto function (df-f1o 5445). For alternate definitions, see dffun2 5448, dffun3 5449, dffun4 5450, dffun5 5451, dffun6 5453, dffun7 5464, dffun8 5465, and dffun9 5466. (Contributed by NM, 1-Aug-1994.)
Assertion
Ref Expression
df-fun

Detailed syntax breakdown of Definition df-fun
StepHypRef Expression
1 cA . . 3
21wfun 5432 . 2
31wrel 4867 . . 3
41ccnv 4861 . . . . 5
51, 4ccom 4866 . . . 4
6 cid 4652 . . . 4
75, 6wss 3365 . . 3
83, 7wa 360 . 2
92, 8wb 178 1
Colors of variables: wff set class
This definition is referenced by:  dffun2  5448  funrel  5455  funss  5456  nffun  5460  funi  5468  funcocnv2  5682  dffv2  5780
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