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Definition df-fun 4985
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 5013). This is not the same as defining a specific function's mapping, which is typically done using the format of cmpt 3876 with the maps-to notation (see df-mpt 3878). Contrast this predicate with the predicates to determine if some class is a function with a given domain (df-fn 4986), a function with a given domain and codomain (df-f 4987), a one-to-one function (df-f1 4988), an onto function (df-fo 4989), or a one-to-one onto function (df-f1o 4990). For alternate definitions, see dffun2 4993, dffun4 4994, dffun6 4997, dffun7 5009, dffun8 5010, and dffun9 5011. (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 4977 . 2 wff Fun 𝐴
31wrel 4418 . . 3 wff Rel 𝐴
41ccnv 4412 . . . . 5 class 𝐴
51, 4ccom 4417 . . . 4 class (𝐴𝐴)
6 cid 4091 . . . 4 class I
75, 6wss 2988 . . 3 wff (𝐴𝐴) ⊆ I
83, 7wa 102 . 2 wff (Rel 𝐴 ∧ (𝐴𝐴) ⊆ I )
92, 8wb 103 1 wff (Fun 𝐴 ↔ (Rel 𝐴 ∧ (𝐴𝐴) ⊆ I ))
Colors of variables: wff set class
This definition is referenced by:  dffun2  4993  funrel  5000  funss  5001  nffun  5005  funi  5013  funcocnv2  5243
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