ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  fnssres Unicode version

Theorem fnssres 4955
Description: Restriction of a function with a subclass of its domain. (Contributed by NM, 2-Aug-1994.)
Assertion
Ref Expression
fnssres  F  Fn  C_  F  |`  Fn

Proof of Theorem fnssres
StepHypRef Expression
1 fnssresb 4954 . 2  F  Fn  F  |`  Fn  C_
21biimpar 281 1  F  Fn  C_  F  |`  Fn
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97    C_ wss 2911    |` cres 4290    Fn wfn 4840
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-14 1402  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-sep 3866  ax-pow 3918  ax-pr 3935
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-rex 2306  df-v 2553  df-un 2916  df-in 2918  df-ss 2925  df-pw 3353  df-sn 3373  df-pr 3374  df-op 3376  df-br 3756  df-opab 3810  df-xp 4294  df-rel 4295  df-cnv 4296  df-co 4297  df-dm 4298  df-res 4300  df-fun 4847  df-fn 4848
This theorem is referenced by:  fnresin1  4956  fnresin2  4957  fssres  5009  fvreseq  5214  fnreseql  5220  ffvresb  5271  fnressn  5292  ofres  5667  tfrlem1  5864  frecrdg  5931  iseqfeq2  8906
  Copyright terms: Public domain W3C validator