Definition df-fun 5189

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 5219). This is not the same as defining a specific function's mapping, which is typically done using the format of cmpt 4042 with the maps-to notation (see df-mpt 4044). Contrast this predicate with the predicates to determine if some class is a function with a given domain (df-fn 5190), a function with a given domain and codomain (df-f 5191), a one-to-one function (df-f1 5192), an onto function (df-fo 5193), or a one-to-one onto function (df-f1o 5194). For alternate definitions, see dffun2 5197, dffun4 5198, dffun6 5201, dffun7 5214, dffun8 5215, and dffun9 5216. (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 5181	. 2 wff Fun A
3	1	wrel 4608	. . 3 wff Rel A
4	1	ccnv 4602	. . . . 5 class `' A
5	1, 4	ccom 4607	. . . 4 class ( A o. `' A )
6		cid 4265	. . . 4 class _I
7	5, 6	wss 3115	. . 3 wff ( A o. `' A ) C_ _I
8	3, 7	wa 103	. 2 wff ( Rel A /\ ( A o. `' A ) C_ _I )
9	2, 8	wb 104	1 wff ( Fun A <-> ( Rel A /\ ( A o. `' A ) C_ _I ) )

This definition is referenced by:  dffun2  5197  funrel  5204  funss  5206  nffun  5210  funi  5219  funcocnv2  5456