Theorem f1ofun 5289

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 5288	. 2 ⊢ (F:A–1-1-onto→B → F Fn A)
2		fnfun 5181	. 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 4775   Fn wfn 4776  –1-1-onto→wf1o 4780

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  df-f1 4792  df-f1o 4794

This theorem is referenced by:  f1ococnv2  5309  enpw1  6062  sbthlem3  6205