Theorem f1ofn 5289

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

Assertion

Ref	Expression
f1ofn	⊢ (F:A–1-1-onto→B → F Fn A)

Proof of Theorem f1ofn

Step	Hyp	Ref	Expression
1		f1of 5288	. 2 ⊢ (F:A–1-1-onto→B → F:A–→B)
2		ffn 5224	. 2 ⊢ (F:A–→B → F Fn A)
3	1, 2	syl 15	1 ⊢ (F:A–1-1-onto→B → F Fn A)

This proof depends on syntax axioms:   → wi 4   Fn wfn 4777  –→wf 4778  –1-1-onto→wf1o 4781

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-an 360  df-f 4792  df-f1 4793  df-f1o 4795

This theorem is used by:  f1ofun  5290  f1odm  5291  f1ofveu  5481  isomin  5497  isoini  5498  nenpw1pwlem2  6086