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Definition df-fun 4827
Description: Define predicate that determines if some class A is a function. Definition 10.1 of [Quine] p. 65. For example, the expression Fun I is true (funi 4854). This is not the same as defining a specific function's mapping, which is typically done using the format of cmpt 3788 with the maps-to notation (see df-mpt 3790). Contrast this predicate with the predicates to determine if some class is a function with a given domain (df-fn 4828), a function with a given domain and codomain (df-f 4829), a one-to-one function (df-f1 4830), an onto function (df-fo 4831), or a one-to-one onto function (df-f1o 4832). For alternate definitions, see dffun2 4835, dffun4 4836, dffun6 4838, dffun7 4850, dffun8 4851, and dffun9 4852. (Contributed by NM, 1-Aug-1994.)
Assertion
Ref Expression
df-fun (Fun A ↔ (Rel A (AA) ⊆ I ))

Detailed syntax breakdown of Definition df-fun
StepHypRef Expression
1 cA . . 3 class A
21wfun 4819 . 2 wff Fun A
31wrel 4273 . . 3 wff Rel A
41ccnv 4267 . . . . 5 class A
51, 4ccom 4272 . . . 4 class (AA)
6 cid 3995 . . . 4 class I
75, 6wss 2890 . . 3 wff (AA) ⊆ I
83, 7wa 97 . 2 wff (Rel A (AA) ⊆ I )
92, 8wb 98 1 wff (Fun A ↔ (Rel A (AA) ⊆ I ))
Colors of variables: wff set class
This definition is referenced by:  dffun2  4835  funrel  4841  funss  4842  nffun  4846  funi  4854  funcocnv2  5072
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