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Definition df-fun 5595
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 13806). This is not the same as defining a specific function's mapping, which is typically done using the format of cmpt 4510 with the maps-to notation (see df-mpt 4512 and df-mpt2 6301). Contrast this predicate with the predicates to determine if some class is a function with a given domain (df-fn 5596), a function with a given domain and codomain (df-f 5597), a one-to-one function (df-f1 5598), an onto function (df-fo 5599), or a one-to-one onto function (df-f1o 5600). For alternate definitions, see dffun2 5603, dffun3 5604, dffun4 5605, dffun5 5606, dffun6 5608, dffun7 5619, dffun8 5620, and dffun9 5621. (Contributed by NM, 1-Aug-1994.)
Assertion
Ref Expression
df-fun

Detailed syntax breakdown of Definition df-fun
StepHypRef Expression
1 cA . . 3
21wfun 5587 . 2
31wrel 5009 . . 3
41ccnv 5003 . . . . 5
51, 4ccom 5008 . . . 4
6 cid 4795 . . . 4
75, 6wss 3475 . . 3
83, 7wa 369 . 2
92, 8wb 184 1
Colors of variables: wff setvar class
This definition is referenced by:  dffun2  5603  funrel  5610  funss  5611  nffun  5615  funi  5623  funcocnv2  5845  dffv2  5946
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