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Definition df-fun 5419
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 13142). This is not the same as defining a specific function's mapping, which is typically done using the format of cmpt 4360 with the maps-to notation (see df-mpt 4362 and df-mpt2 6072). Contrast this predicate with the predicates to determine if some class is a function with a given domain (df-fn 5420), a function with a given domain and codomain (df-f 5421), a one-to-one function (df-f1 5422), an onto function (df-fo 5423), or a one-to-one onto function (df-f1o 5424). For alternate definitions, see dffun2 5427, dffun3 5428, dffun4 5429, dffun5 5430, dffun6 5432, dffun7 5443, dffun8 5444, and dffun9 5445. (Contributed by NM, 1-Aug-1994.)
Assertion
Ref Expression
df-fun

Detailed syntax breakdown of Definition df-fun
StepHypRef Expression
1 cA . . 3
21wfun 5411 . 2
31wrel 4849 . . 3
41ccnv 4843 . . . . 5
51, 4ccom 4848 . . . 4
6 cid 4634 . . . 4
75, 6wss 3353 . . 3
83, 7wa 360 . 2
92, 8wb 178 1
Colors of variables: wff set class
This definition is referenced by:  dffun2  5427  funrel  5434  funss  5435  nffun  5439  funi  5447  funcocnv2  5659  dffv2  5757
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