Theorem f1rn 5404

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 5403	. 2 |- ( F : A -1-1-> B -> F : A --> B )
2		frn 5356	. 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 3121   ran crn 4612   -->wf 5194   -1-1->wf1 5195

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106

This theorem depends on definitions:  df-bi 116  df-f 5202  df-f1 5203

This theorem is referenced by:  fun11iun  5463  f1dmex  6095  f1finf1o  6924  caserel  7064  djudom  7070  exmidfodomrlemim  7178