Theorem frnd 5347

Description: Deduction form of frn 5346. 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 5346	. 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 3116   ran crn 4605   -->wf 5184

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 5192

This theorem is referenced by:  difinfsn  7065  ennnfonelemfun  12350  ennnfonelemf1  12351  tgrest  12819  resttopon  12821  rest0  12829  cnrest2r  12887  cnptoprest2  12890  lmss  12896  txbasval  12917  upxp  12922  uptx  12924  hmeores  12965  unirnblps  13072  unirnbl  13073