Theorem ffun 5048

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 5046	. 2 |- ( F : A --> B -> F Fn A )
2		fnfun 4996	. 2 |- ( F Fn A -> Fun F )
3	1, 2	syl 14	1 |- ( F : A --> B -> Fun F )

Syntax hints:   -> wi 4   Fun wfun 4896   Fn wfn 4897   -->wf 4898

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99

This theorem depends on definitions:  df-bi 110  df-fn 4905  df-f 4906

This theorem is referenced by:  funssxp  5060  f00  5081  fofun  5107  fun11iun  5147  fimacnv  5296  dff3im  5312  fmptco  5330  fliftf  5439  smores2  5909  ac6sfi  6352  nn0supp  8234  climdm  9816