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Definition df-fun 4271
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 10671). This is not the same as defining a specific function's mapping, which is typically done using the format of cmpt 5459 with the maps-to notation (see df-mpt 5461 and df-mpt2 5462). Contrast this predicate with the predicates to determine if some class is a function with a given domain (df-fn 4272), a function with a given domain and codomain (df-f 4273), a one-to-one function (df-f1 4274), an onto function (df-fo 4275), or a one-to-one onto function (df-f1o 4276). For alternate definitions, see dffun2 4748, dffun3 4749, dffun4 4750, dffun5 4751, dffun6 4753, dffun7 4763, dffun8 4764, and dffun9 4765.
Assertion
Ref Expression
df-fun

Detailed syntax breakdown of Definition df-fun
StepHypRef Expression
1 cA . . 3
21wfun 4255 . 2
31wrel 4254 . . 3
41ccnv 4248 . . . . 5
51, 4ccom 4253 . . . 4
6 cid 3843 . . . 4
75, 6wss 2810 . . 3
83, 7wa 357 . 2
92, 8wb 174 1
Colors of variables: wff set class
This definition is referenced by:  dffun2  4748  funrel  4755  funss  4756  hbfun  4760  funi  4767  funcocnv2  4970  dffv2  5050
Copyright terms: Public domain