Theorem ffun 4991

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 4989	. 2 |- ( F :A -->B -> F Fn A)
2		fnfun 4939	. 2 |- ( F Fn A -> Fun F)
3	1, 2	syl 14	1 |- ( F :A -->B -> Fun F)

Syntax hints:   -> wi 4   Fun wfun 4839   Fn wfn 4840   -->wf 4841

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 4848  df-f 4849

This theorem is referenced by:  funssxp  5003  f00  5024  fofun  5050  fun11iun  5090  fimacnv  5239  dff3im  5255  fmptco  5273  fliftf  5382  smores2  5850  nn0supp  8010