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

Theorem elcnv 4858
 Description: Membership in a converse. Equation 5 of [Suppes] p. 62. (Contributed by NM, 24-Mar-1998.)
Assertion
Ref Expression
elcnv
Distinct variable groups:   ,,   ,,

Proof of Theorem elcnv
StepHypRef Expression
1 df-cnv 4697 . . 3
21eleq2i 2347 . 2
3 elopab 4272 . 2
42, 3bitri 240 1
 Colors of variables: wff set class Syntax hints:   wb 176   wa 358  wex 1528   wceq 1623   wcel 1684  cop 3643   class class class wbr 4023  copab 4076  ccnv 4688 This theorem is referenced by:  elcnv2  4859 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-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  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-opab 4078  df-cnv 4697
 Copyright terms: Public domain W3C validator