Theorem f1fn 5260

Description: A one-to-one mapping is a function on its domain. (Contributed by set.mm contributors, 8-Mar-2014.)

Assertion

Ref	Expression
f1fn	⊢ (F:A–1-1→B → F Fn A)

Proof of Theorem f1fn

Step	Hyp	Ref	Expression
1		f1f 5259	. 2 ⊢ (F:A–1-1→B → F:A–→B)
2		ffn 5224	. 2 ⊢ (F:A–→B → F Fn A)
3	1, 2	syl 15	1 ⊢ (F:A–1-1→B → F Fn A)

This proof depends on syntax axioms:   → wi 4   Fn wfn 4777  –→wf 4778  –1-1→wf1 4779

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

This theorem is used by:  f1fun  5261  f1dm  5262  f1f1orn  5298  f1elima  5475