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Definition df-fun 5539
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 13514). This is not the same as defining a specific function's mapping, which is typically done using the format of cmpt 4467 with the maps-to notation (see df-mpt 4469 and df-mpt2 6227). Contrast this predicate with the predicates to determine if some class is a function with a given domain (df-fn 5540), a function with a given domain and codomain (df-f 5541), a one-to-one function (df-f1 5542), an onto function (df-fo 5543), or a one-to-one onto function (df-f1o 5544). For alternate definitions, see dffun2 5547, dffun3 5548, dffun4 5549, dffun5 5550, dffun6 5552, dffun7 5563, dffun8 5564, and dffun9 5565. (Contributed by NM, 1-Aug-1994.)
Assertion
Ref Expression
df-fun

Detailed syntax breakdown of Definition df-fun
StepHypRef Expression
1 cA . . 3
21wfun 5531 . 2
31wrel 4962 . . 3
41ccnv 4956 . . . . 5
51, 4ccom 4961 . . . 4
6 cid 4748 . . . 4
75, 6wss 3442 . . 3
83, 7wa 369 . 2
92, 8wb 184 1
Colors of variables: wff setvar class
This definition is referenced by:  dffun2  5547  funrel  5554  funss  5555  nffun  5559  funi  5567  funcocnv2  5787  dffv2  5887
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