Theorem frnd 39426

Description: The range of a mapping. (Contributed by Glauco Siliprandi, 26-Jun-2021.)

Hypothesis

Ref	Expression
frnd.1	|- ( ph -> F : A --> B )

Assertion

Ref	Expression
frnd	|- ( ph -> ran F C_ B )

Proof of Theorem frnd

Step	Hyp	Ref	Expression
1		frnd.1	. 2 |- ( ph -> F : A --> B )
2		frn 6053	. 2 |- ( F : A --> B -> ran F C_ B )
3	1, 2	syl 17	1 |- ( ph -> ran F C_ B )

Syntax hints:   -> wi 4   C_ wss 3574   ran crn 5115   -->wf 5884

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

This theorem depends on definitions:  df-bi 197  df-an 386  df-f 5892

This theorem is referenced by:  climinf2lem  39938  limsupvaluz2  39970  supcnvlimsup  39972  limsupgtlem  40009  preimaioomnf  40929  smfco  41009