Definition df-fun 5274

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 5304). This is not the same as defining a specific function's mapping, which is typically done using the format of cmpt 4106 with the maps-to notation (see df-mpt 4108). Contrast this predicate with the predicates to determine if some class is a function with a given domain (df-fn 5275), a function with a given domain and codomain (df-f 5276), a one-to-one function (df-f1 5277), an onto function (df-fo 5278), or a one-to-one onto function (df-f1o 5279). For alternate definitions, see dffun2 5282, dffun4 5283, dffun6 5286, dffun7 5299, dffun8 5300, and dffun9 5301. (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 5266	. 2 wff Fun A
3	1	wrel 4681	. . 3 wff Rel A
4	1	ccnv 4675	. . . . 5 class `' A
5	1, 4	ccom 4680	. . . 4 class ( A o. `' A )
6		cid 4336	. . . 4 class _I
7	5, 6	wss 3166	. . 3 wff ( A o. `' A ) C_ _I
8	3, 7	wa 104	. 2 wff ( Rel A /\ ( A o. `' A ) C_ _I )
9	2, 8	wb 105	1 wff ( Fun A <-> ( Rel A /\ ( A o. `' A ) C_ _I ) )

This definition is referenced by:  dffun2  5282  funrel  5289  funss  5291  nffun  5295  funi  5304  funcocnv2  5549