Definition df-dfat 30020

Description: Definition of the predicate that determines if some class F is defined as function for an argument A or, in other words, if the function value for some class F for an argument A is defined. We say that F is defined at A if a F is a function restricted to the member A of its domain. (Contributed by Alexander van der Vekens, 25-May-2017.)

Assertion

Ref	Expression
df-dfat	|- ( F defAt A <-> ( A e. dom F /\ Fun ( F |` { A } ) ) )

Detailed syntax breakdown of Definition df-dfat

Step	Hyp	Ref	Expression
1		cA	. . 3 class A
2		cF	. . 3 class F
3	1, 2	wdfat 30017	. 2 wff F defAt A
4	2	cdm 4840	. . . 4 class dom F
5	1, 4	wcel 1756	. . 3 wff A e. dom F
6	1	csn 3877	. . . . 5 class { A }
7	2, 6	cres 4842	. . . 4 class ( F |` { A } )
8	7	wfun 5412	. . 3 wff Fun ( F |` { A } )
9	5, 8	wa 369	. 2 wff ( A e. dom F /\ Fun ( F |` { A } ) )
10	3, 9	wb 184	1 wff ( F defAt A <-> ( A e. dom F /\ Fun ( F |` { A } ) ) )

This definition is referenced by:  dfateq12d  30035  nfdfat  30036  dfdfat2  30037  ndmafv  30046  nfunsnafv  30048  afvpcfv0  30052  afvfvn0fveq  30056  afv0nbfvbi  30057  fnbrafvb  30060  afvelrn  30074  afvres  30078  tz6.12-afv  30079  dmfcoafv  30081  afvco2  30082  aovmpt4g  30107