ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  dfrn4 GIF version

Theorem dfrn4 4809
Description: Range defined in terms of image. (Contributed by NM, 14-May-2008.)
Assertion
Ref Expression
dfrn4 ran 𝐴 = (𝐴 “ V)

Proof of Theorem dfrn4
StepHypRef Expression
1 df-ima 4386 . 2 (𝐴 “ V) = ran (𝐴 ↾ V)
2 rnresv 4808 . 2 ran (𝐴 ↾ V) = ran 𝐴
31, 2eqtr2i 2077 1 ran 𝐴 = (𝐴 “ V)
Colors of variables: wff set class
Syntax hints:   = wceq 1259  Vcvv 2574  ran crn 4374  cres 4375  cima 4376
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-14 1421  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038  ax-sep 3903  ax-pow 3955  ax-pr 3972
This theorem depends on definitions:  df-bi 114  df-3an 898  df-tru 1262  df-nf 1366  df-sb 1662  df-eu 1919  df-mo 1920  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-ral 2328  df-rex 2329  df-v 2576  df-un 2950  df-in 2952  df-ss 2959  df-pw 3389  df-sn 3409  df-pr 3410  df-op 3412  df-br 3793  df-opab 3847  df-xp 4379  df-rel 4380  df-cnv 4381  df-dm 4383  df-rn 4384  df-res 4385  df-ima 4386
This theorem is referenced by:  dmmpt  4844
  Copyright terms: Public domain W3C validator