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Definition df-fun 6099
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 15017). This is not the same as defining a specific function's mapping, which is typically done using the format of cmpt 4923 with the maps-to notation (see df-mpt 4924 and df-mpt2 6875). Contrast this predicate with the predicates to determine if some class is a function with a given domain (df-fn 6100), a function with a given domain and codomain (df-f 6101), a one-to-one function (df-f1 6102), an onto function (df-fo 6103), or a one-to-one onto function (df-f1o 6104). For alternate definitions, see dffun2 6107, dffun3 6108, dffun4 6109, dffun5 6110, dffun6 6112, dffun7 6124, dffun8 6125, and dffun9 6126. (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 6091 . 2 wff Fun 𝐴
31wrel 5316 . . 3 wff Rel 𝐴
41ccnv 5310 . . . . 5 class 𝐴
51, 4ccom 5315 . . . 4 class (𝐴𝐴)
6 cid 5218 . . . 4 class I
75, 6wss 3769 . . 3 wff (𝐴𝐴) ⊆ I
83, 7wa 384 . 2 wff (Rel 𝐴 ∧ (𝐴𝐴) ⊆ I )
92, 8wb 197 1 wff (Fun 𝐴 ↔ (Rel 𝐴 ∧ (𝐴𝐴) ⊆ I ))
Colors of variables: wff setvar class
This definition is referenced by:  dffun2  6107  funrel  6114  funss  6116  nffun  6120  funi  6129  funcocnv2  6373  dffv2  6488
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