Theorem f1f 5258

Description: A one-to-one mapping is a mapping. (Contributed by set.mm contributors, 31-Dec-1996.)

Assertion

Ref	Expression
f1f	⊢ (F:A–1-1→B → F:A–→B)

Proof of Theorem f1f

Step	Hyp	Ref	Expression
1		df-f1 4792	. 2 ⊢ (F:A–1-1→B ↔ (F:A–→B ∧ Fun ◡F))
2	1	simplbi 446	1 ⊢ (F:A–1-1→B → F:A–→B)

Syntax hints:   → wi 4  ^◡ccnv 4771  Fun wfun 4775  –→wf 4777  –1-1→wf1 4778

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8

This theorem depends on definitions:  df-bi 177  df-an 360  df-f1 4792

This theorem is referenced by:  f1fn  5259  f1ss  5262  f1of  5287  dff1o5  5295  fun11iun  5305  dflec3  6221