Theorem f1ofun 5290

Description: A one-to-one onto mapping is a function. (Contributed by set.mm contributors, 12-Dec-2003.)

Assertion

Ref	Expression
f1ofun	|- (F:A-1-1-onto->B -> Fun F)

Proof of Theorem f1ofun

Step	Hyp	Ref	Expression
1		f1ofn 5289	. 2 |- (F:A-1-1-onto->B -> F Fn A)
2		fnfun 5182	. 2 |- (F Fn A -> Fun F)
3	1, 2	syl 15	1 |- (F:A-1-1-onto->B -> Fun F)

Syntax hints:   -> wi 4  Fun wfun 4776   Fn wfn 4777  -1-1-onto->wf1o 4781

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  df-f1 4793  df-f1o 4795

This theorem is referenced by:  f1ococnv2  5310  enpw1  6063  sbthlem3  6206