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

Theorem eldm 4475
Description: Membership in a domain. Theorem 4 of [Suppes] p. 59. (Contributed by NM, 2-Apr-2004.)
Hypothesis
Ref Expression
eldm.1  _V
Assertion
Ref Expression
eldm  dom
Distinct variable groups:   ,   ,

Proof of Theorem eldm
StepHypRef Expression
1 eldm.1 . 2  _V
2 eldmg 4473 . 2  _V  dom
31, 2ax-mp 7 1  dom
Colors of variables: wff set class
Syntax hints:   wb 98  wex 1378   wcel 1390   _Vcvv 2551   class class class wbr 3755   dom cdm 4288
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-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
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-v 2553  df-un 2916  df-sn 3373  df-pr 3374  df-op 3376  df-br 3756  df-dm 4298
This theorem is referenced by:  dmi  4493  dmcoss  4544  dmcosseq  4546  dminss  4681  dmsnm  4729  dffun7  4871  dffun8  4872  fnres  4958  fndmdif  5215  reldmtpos  5809  dmtpos  5812  tfrexlem  5889
  Copyright terms: Public domain W3C validator