Definition df-fun 5174

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 5204). This is not the same as defining a specific function's mapping, which is typically done using the format of cmpt 4027 with the maps-to notation (see df-mpt 4029). Contrast this predicate with the predicates to determine if some class is a function with a given domain (df-fn 5175), a function with a given domain and codomain (df-f 5176), a one-to-one function (df-f1 5177), an onto function (df-fo 5178), or a one-to-one onto function (df-f1o 5179). For alternate definitions, see dffun2 5182, dffun4 5183, dffun6 5186, dffun7 5199, dffun8 5200, and dffun9 5201. (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 5166	. 2 wff Fun A
3	1	wrel 4593	. . 3 wff Rel A
4	1	ccnv 4587	. . . . 5 class `' A
5	1, 4	ccom 4592	. . . 4 class ( A o. `' A )
6		cid 4250	. . . 4 class _I
7	5, 6	wss 3102	. . 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  5182  funrel  5189  funss  5191  nffun  5195  funi  5204  funcocnv2  5441