Theorem frnd 5238

Description: Deduction form of frn 5237. 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 5237	. 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 3035   ran crn 4498   -->wf 5075

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

This theorem depends on definitions:  df-bi 116  df-f 5083

This theorem is referenced by:  difinfsn  6935  ennnfonelemfun  11769  ennnfonelemf1  11770  tgrest  12175  resttopon  12177  rest0  12185  cnrest2r  12242  cnptoprest2  12245  lmss  12251  txbasval  12272  upxp  12277  uptx  12279  unirnblps  12405  unirnbl  12406