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Definition df-fun 5132
 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 5162). This is not the same as defining a specific function's mapping, which is typically done using the format of cmpt 3996 with the maps-to notation (see df-mpt 3998). Contrast this predicate with the predicates to determine if some class is a function with a given domain (df-fn 5133), a function with a given domain and codomain (df-f 5134), a one-to-one function (df-f1 5135), an onto function (df-fo 5136), or a one-to-one onto function (df-f1o 5137). For alternate definitions, see dffun2 5140, dffun4 5141, dffun6 5144, dffun7 5157, dffun8 5158, and dffun9 5159. (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 5124 . 2 wff Fun 𝐴
31wrel 4551 . . 3 wff Rel 𝐴
41ccnv 4545 . . . . 5 class 𝐴
51, 4ccom 4550 . . . 4 class (𝐴𝐴)
6 cid 4217 . . . 4 class I
75, 6wss 3075 . . 3 wff (𝐴𝐴) ⊆ I
83, 7wa 103 . 2 wff (Rel 𝐴 ∧ (𝐴𝐴) ⊆ I )
92, 8wb 104 1 wff (Fun 𝐴 ↔ (Rel 𝐴 ∧ (𝐴𝐴) ⊆ I ))
 Colors of variables: wff set class This definition is referenced by:  dffun2  5140  funrel  5147  funss  5149  nffun  5153  funi  5162  funcocnv2  5399
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