Theorem ffun 5068

Description: A mapping is a function. (Contributed by NM, 3-Aug-1994.)

Assertion

Ref	Expression
ffun	|- ( F : A --> B -> Fun F )

Proof of Theorem ffun

Step	Hyp	Ref	Expression
1		ffn 5066	. 2 |- ( F : A --> B -> F Fn A )
2		fnfun 5016	. 2 |- ( F Fn A -> Fun F )
3	1, 2	syl 14	1 |- ( F : A --> B -> Fun F )

Syntax hints:   -> wi 4   Fun wfun 4916   Fn wfn 4917   -->wf 4918

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104

This theorem depends on definitions:  df-bi 115  df-fn 4925  df-f 4926

This theorem is referenced by:  funssxp  5080  f00  5101  fofun  5127  fun11iun  5167  fimacnv  5317  dff3im  5333  fmptco  5351  fliftf  5459  smores2  5932  ac6sfi  6379  nn0supp  8340  climdm  10134