Theorem frnd 5282

Description: Deduction form of frn 5281. 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 5281	. 2 |- ( F : A --> B -> ran F C_ B )
3	1, 2	syl 14	1 |- ( ph -> ran F C_ B )

Syntax hints:   -> wi 4   C_ wss 3071   ran crn 4540   -->wf 5119

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 5127

This theorem is referenced by:  difinfsn  6985  ennnfonelemfun  11930  ennnfonelemf1  11931  tgrest  12338  resttopon  12340  rest0  12348  cnrest2r  12406  cnptoprest2  12409  lmss  12415  txbasval  12436  upxp  12441  uptx  12443  hmeores  12484  unirnblps  12591  unirnbl  12592