Theorem ffun 5226

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

Assertion

Ref	Expression
ffun	⊢ (F:A–→B → Fun F)

Proof of Theorem ffun

Step	Hyp	Ref	Expression
1		ffn 5224	. 2 ⊢ (F:A–→B → F Fn A)
2		fnfun 5182	. 2 ⊢ (F Fn A → Fun F)
3	1, 2	syl 15	1 ⊢ (F:A–→B → Fun F)

Syntax hints:   → wi 4  Fun wfun 4776   Fn wfn 4777  –→wf 4778

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360  df-fn 4791  df-f 4792

This theorem is referenced by:  funssxp  5234  f00  5250  fofun  5271  f1ores  5301  fimacnv  5412  dff3  5421  mapsspm  6022  xpsnen  6050  enprmaplem3  6079