Theorem f1rn 5599

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 5598	. 2 |- ( F : A -1-1-> B -> F : A --> B )
2		frn 5542	. 2 |- ( F : A --> B -> ran F C_ B )
3	1, 2	syl 14	1 |- ( F : A -1-1-> B -> ran F C_ B )

This proof depends on syntax axioms:   -> wi 4   C_ wss 3220   ran crn 4775   -->wf 5373   -1-1->wf1 5374

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107

This proof depends on definitions:  df-bi 117  df-f 5381  df-f1 5382

This theorem is used by:  fun11iun  5660  f1dmex  6345  f1finf1o  7264  caserel  7427  djudom  7433  exmidfodomrlemim  7553  hashf1lem2  11286  usgruspgrben  16427  domomsubct  17031