HomeHome Metamath Proof Explorer < Previous   Next >
Related theorems
Unicode version

Definition df-fun 4009
Description: Define a function. Definition 10.1 of [Quine] p. 65. For alternate definitions, see dffun2 4439, dffun3 4440, dffun4 4441, dffun5 4442, dffun6 4444, dffun7 4454, dffun8 4455, and dffun9 4456.
Assertion
Ref Expression
df-fun |- (Fun A <-> (Rel A /\ (A o. `'A) C_ _I ))

Detailed syntax breakdown of Definition df-fun
StepHypRef Expression
1 cA . . 3 class A
21wfun 3993 . 2 wff Fun A
31wrel 3992 . . 3 wff Rel A
41ccnv 3986 . . . . 5 class `'A
51, 4ccom 3991 . . . 4 class (A o. `'A)
6 cid 3603 . . . 4 class _I
75, 6wss 2636 . . 3 wff (A o. `'A) C_ _I
83, 7wa 357 . 2 wff (Rel A /\ (A o. `'A) C_ _I )
92, 8wb 174 1 wff (Fun A <-> (Rel A /\ (A o. `'A) C_ _I ))
Colors of variables: wff set class
This definition is referenced by:  dffun2 4439  funrel 4446  funss 4447  hbfun 4451  funi 4458  f1ococnv2 4645  dffv2 4722  flimfnei2 16233  cnvcan 17138
Copyright terms: Public domain