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Theorem elcnv 5169
 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 4997 . . 3
21eleq2i 2521 . 2
3 elopab 4745 . 2
42, 3bitri 249 1
 Colors of variables: wff setvar class Syntax hints:   wb 184   wa 369   wceq 1383  wex 1599   wcel 1804  cop 4020   class class class wbr 4437  copab 4494  ccnv 4988 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-9 1808  ax-10 1823  ax-11 1828  ax-12 1840  ax-13 1985  ax-ext 2421  ax-sep 4558  ax-nul 4566  ax-pr 4676 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 976  df-tru 1386  df-ex 1600  df-nf 1604  df-sb 1727  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2593  df-ne 2640  df-v 3097  df-dif 3464  df-un 3466  df-in 3468  df-ss 3475  df-nul 3771  df-if 3927  df-sn 4015  df-pr 4017  df-op 4021  df-opab 4496  df-cnv 4997 This theorem is referenced by:  elcnv2  5170  gsummpt2co  27749
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