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Definition df-fun 5392
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 13296). This is not the same as defining a specific function's mapping, which is typically done using the format of cmpt 4325 with the maps-to notation (see df-mpt 4327 and df-mpt2 6066). Contrast this predicate with the predicates to determine if some class is a function with a given domain (df-fn 5393), a function with a given domain and codomain (df-f 5394), a one-to-one function (df-f1 5395), an onto function (df-fo 5396), or a one-to-one onto function (df-f1o 5397). For alternate definitions, see dffun2 5400, dffun3 5401, dffun4 5402, dffun5 5403, dffun6 5405, dffun7 5416, dffun8 5417, and dffun9 5418. (Contributed by NM, 1-Aug-1994.)
Assertion
Ref Expression
df-fun

Detailed syntax breakdown of Definition df-fun
StepHypRef Expression
1 cA . . 3
21wfun 5384 . 2
31wrel 4816 . . 3
41ccnv 4810 . . . . 5
51, 4ccom 4815 . . . 4
6 cid 4602 . . . 4
75, 6wss 3305 . . 3
83, 7wa 362 . 2
92, 8wb 178 1
Colors of variables: wff setvar class
This definition is referenced by:  dffun2  5400  funrel  5407  funss  5408  nffun  5412  funi  5420  funcocnv2  5635  dffv2  5734
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