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Definition df-fun 6351
Description: Define predicate that determines if some class 𝐴 is a function. Definition 10.1 of [Quine] p. 65. For example, the expression Fun cos is true once we define cosine (df-cos 15414). This is not the same as defining a specific function's mapping, which is typically done using the format of cmpt 5138 with the maps-to notation (see df-mpt 5139 and df-mpo 7150). Contrast this predicate with the predicates to determine if some class is a function with a given domain (df-fn 6352), a function with a given domain and codomain (df-f 6353), a one-to-one function (df-f1 6354), an onto function (df-fo 6355), or a one-to-one onto function (df-f1o 6356). For alternate definitions, see dffun2 6359, dffun3 6360, dffun4 6361, dffun5 6362, dffun6 6364, dffun7 6376, dffun8 6377, and dffun9 6378. (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 6343 . 2 wff Fun 𝐴
31wrel 5554 . . 3 wff Rel 𝐴
41ccnv 5548 . . . . 5 class 𝐴
51, 4ccom 5553 . . . 4 class (𝐴𝐴)
6 cid 5453 . . . 4 class I
75, 6wss 3935 . . 3 wff (𝐴𝐴) ⊆ I
83, 7wa 396 . 2 wff (Rel 𝐴 ∧ (𝐴𝐴) ⊆ I )
92, 8wb 207 1 wff (Fun 𝐴 ↔ (Rel 𝐴 ∧ (𝐴𝐴) ⊆ I ))
Colors of variables: wff setvar class
This definition is referenced by:  dffun2  6359  funrel  6366  funss  6368  nffun  6372  funi  6381  funcocnv2  6633  dffv2  6750  funALTVfun  35813
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