Definition df-fun 4924

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 4952). This is not the same as defining a specific function's mapping, which is typically done using the format of cmpt 3839 with the maps-to notation (see df-mpt 3841). Contrast this predicate with the predicates to determine if some class is a function with a given domain (df-fn 4925), a function with a given domain and codomain (df-f 4926), a one-to-one function (df-f1 4927), an onto function (df-fo 4928), or a one-to-one onto function (df-f1o 4929). For alternate definitions, see dffun2 4932, dffun4 4933, dffun6 4936, dffun7 4948, dffun8 4949, and dffun9 4950. (Contributed by NM, 1-Aug-1994.)

Assertion

Ref	Expression
df-fun	|- ( Fun A <-> ( Rel A /\ ( A o. `' A ) C_ _I ) )

Detailed syntax breakdown of Definition df-fun

Step	Hyp	Ref	Expression
1		cA	. . 3 class A
2	1	wfun 4916	. 2 wff Fun A
3	1	wrel 4368	. . 3 wff Rel A
4	1	ccnv 4362	. . . . 5 class `' A
5	1, 4	ccom 4367	. . . 4 class ( A o. `' A )
6		cid 4043	. . . 4 class _I
7	5, 6	wss 2973	. . 3 wff ( A o. `' A ) C_ _I
8	3, 7	wa 102	. 2 wff ( Rel A /\ ( A o. `' A ) C_ _I )
9	2, 8	wb 103	1 wff ( Fun A <-> ( Rel A /\ ( A o. `' A ) C_ _I ) )

This definition is referenced by:  dffun2  4932  funrel  4939  funss  4940  nffun  4944  funi  4952  funcocnv2  5171