Theorem f1rn 5543

Description: The range of a one-to-one mapping. (Contributed by BJ, 6-Jul-2022.)

Assertion

Ref	Expression
f1rn	|- ( F : A -1-1-> B -> ran F C_ B )

Proof of Theorem f1rn

Step	Hyp	Ref	Expression
1		f1f 5542	. 2 |- ( F : A -1-1-> B -> F : A --> B )
2		frn 5491	. 2 |- ( F : A --> B -> ran F C_ B )
3	1, 2	syl 14	1 |- ( F : A -1-1-> B -> ran F C_ B )

Syntax hints:   -> wi 4   C_ wss 3200   ran crn 4726   -->wf 5322   -1-1->wf1 5323

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107

This theorem depends on definitions:  df-bi 117  df-f 5330  df-f1 5331

This theorem is referenced by:  fun11iun  5604  f1dmex  6278  f1finf1o  7146  caserel  7286  djudom  7292  exmidfodomrlemim  7412  usgruspgrben  16056  domomsubct  16653