Theorem ffun 5225

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 5223	. 2 ⊢ (F:A–→B → F Fn A)
2		fnfun 5181	. 2 ⊢ (F Fn A → Fun F)
3	1, 2	syl 15	1 ⊢ (F:A–→B → Fun F)

Syntax hints:   → wi 4  Fun wfun 4775   Fn wfn 4776  –→wf 4777

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 4790  df-f 4791

This theorem is referenced by:  funssxp  5233  f00  5249  fofun  5270  f1ores  5300  fimacnv  5411  dff3  5420  mapsspm  6021  xpsnen  6049  enprmaplem3  6078