ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  df-fun GIF version

Definition df-fun 4882
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 4910). This is not the same as defining a specific function's mapping, which is typically done using the format of cmpt 3815 with the maps-to notation (see df-mpt 3817). Contrast this predicate with the predicates to determine if some class is a function with a given domain (df-fn 4883), a function with a given domain and codomain (df-f 4884), a one-to-one function (df-f1 4885), an onto function (df-fo 4886), or a one-to-one onto function (df-f1o 4887). For alternate definitions, see dffun2 4890, dffun4 4891, dffun6 4894, dffun7 4906, dffun8 4907, and dffun9 4908. (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 4874 . 2 wff Fun 𝐴
31wrel 4328 . . 3 wff Rel 𝐴
41ccnv 4322 . . . . 5 class 𝐴
51, 4ccom 4327 . . . 4 class (𝐴𝐴)
6 cid 4022 . . . 4 class I
75, 6wss 2914 . . 3 wff (𝐴𝐴) ⊆ I
83, 7wa 97 . 2 wff (Rel 𝐴 ∧ (𝐴𝐴) ⊆ I )
92, 8wb 98 1 wff (Fun 𝐴 ↔ (Rel 𝐴 ∧ (𝐴𝐴) ⊆ I ))
Colors of variables: wff set class
This definition is referenced by:  dffun2  4890  funrel  4897  funss  4898  nffun  4902  funi  4910  funcocnv2  5129
  Copyright terms: Public domain W3C validator