Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  dfrn2 Unicode version

Theorem dfrn2 4868
 Description: Alternate definition of range. Definition 4 of [Suppes] p. 60. (Contributed by NM, 27-Dec-1996.)
Assertion
Ref Expression
dfrn2
Distinct variable group:   ,,

Proof of Theorem dfrn2
StepHypRef Expression
1 df-rn 4700 . 2
2 df-dm 4699 . 2
3 vex 2791 . . . . 5
4 vex 2791 . . . . 5
53, 4brcnv 4864 . . . 4
65exbii 1569 . . 3
76abbii 2395 . 2
81, 2, 73eqtri 2307 1
 Colors of variables: wff set class Syntax hints:  wex 1528   wceq 1623  cab 2269   class class class wbr 4023  ccnv 4688   cdm 4689   crn 4690 This theorem is referenced by:  dfrn3  4869  dfdm4  4872  dm0rn0  4895  dfrnf  4917  dfima2  5014  funcnv3  5311 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-br 4024  df-opab 4078  df-cnv 4697  df-dm 4699  df-rn 4700
 Copyright terms: Public domain W3C validator