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Definition df-fun 5491
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 12711). This is not the same as defining a specific function's mapping, which is typically done using the format of cmpt 4297 with the maps-to notation (see df-mpt 4299 and df-mpt2 6122). Contrast this predicate with the predicates to determine if some class is a function with a given domain (df-fn 5492), a function with a given domain and codomain (df-f 5493), a one-to-one function (df-f1 5494), an onto function (df-fo 5495), or a one-to-one onto function (df-f1o 5496). For alternate definitions, see dffun2 5499, dffun3 5500, dffun4 5501, dffun5 5502, dffun6 5504, dffun7 5514, dffun8 5515, and dffun9 5516. (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 5483 . 2 wff Fun 𝐴
31wrel 4918 . . 3 wff Rel 𝐴
41ccnv 4912 . . . . 5 class 𝐴
51, 4ccom 4917 . . . 4 class (𝐴𝐴)
6 cid 4528 . . . 4 class I
75, 6wss 3309 . . 3 wff (𝐴𝐴) ⊆ I
83, 7wa 360 . 2 wff (Rel 𝐴 ∧ (𝐴𝐴) ⊆ I )
92, 8wb 178 1 wff (Fun 𝐴 ↔ (Rel 𝐴 ∧ (𝐴𝐴) ⊆ I ))
Colors of variables: wff set class
This definition is referenced by:  dffun2  5499  funrel  5506  funss  5507  nffun  5511  funi  5518  funcocnv2  5735  dffv2  5832
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