Definition df-dfat 32362

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 32359	. 2 wff F defAt A
4	2	cdm 5008	. . . 4 class dom F
5	1, 4	wcel 1819	. . 3 wff A e. dom F
6	1	csn 4032	. . . . 5 class { A }
7	2, 6	cres 5010	. . . 4 class ( F |` { A } )
8	7	wfun 5588	. . 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  32375  nfdfat  32376  dfdfat2  32377  ndmafv  32386  nfunsnafv  32388  afvpcfv0  32392  afvfvn0fveq  32396  afv0nbfvbi  32397  fnbrafvb  32400  afvelrn  32414  afvres  32418  tz6.12-afv  32419  dmfcoafv  32421  afvco2  32422  aovmpt4g  32447