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Definition df-fun 5503
Description: Define predicate that determines if some class is a function. Definition 10.1 of [Quine] p. 65. For example, the expression ?Error: cos ^^^ This math symbol is not active (i.e. was not declared in this scope). Fun is true once we define cosine (df-cos 12724). This is not the same as defining a specific function's mapping, which is typically done using the format of cmpt 4301 with the maps-to notation (see df-mpt 4303 and df-mpt2 6134). Contrast this predicate with the predicates to determine if some class is a function with a given domain (df-fn 5504), a function with a given domain and codomain (df-f 5505), a one-to-one function (df-f1 5506), an onto function (df-fo 5507), or a one-to-one onto function (df-f1o 5508). For alternate definitions, see dffun2 5511, dffun3 5512, dffun4 5513, dffun5 5514, dffun6 5516, dffun7 5526, dffun8 5527, and dffun9 5528. (Contributed by NM, 1-Aug-1994.)
Assertion
Ref Expression
df-fun

Detailed syntax breakdown of Definition df-fun
StepHypRef Expression
1 cA . . 3
21wfun 5495 . 2
31wrel 4924 . . 3
41ccnv 4918 . . . . 5
51, 4ccom 4923 . . . 4
6 cid 4534 . . . 4
75, 6wss 3309 . . 3
83, 7wa 360 . 2
92, 8wb 178 1
Colors of variables: wff set class
This definition is referenced by:  dffun2  5511  funrel  5518  funss  5519  nffun  5523  funi  5530  funcocnv2  5747  dffv2  5844
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