Mathbox for Rodolfo Medina < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  eqrelrdvOLD Unicode version

Theorem eqrelrdvOLD 25876
 Description: Deduce equality of relations from equivalence of membership. (Moved to eqrelrdv 4820 in main set.mm and may be deleted by mathbox owner, RM. --NM 20-Feb-2014.) (Contributed by Rodolfo Medina, 10-Oct-2010.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
eqrelrdvOLD.1
eqrelrdvOLD.2
eqrelrdvOLD.3
Assertion
Ref Expression
eqrelrdvOLD
Distinct variable groups:   ,,   ,,   ,,

Proof of Theorem eqrelrdvOLD
StepHypRef Expression
1 eqrelrdvOLD.3 . . 3
21alrimivv 1623 . 2
3 eqrelrdvOLD.1 . . 3
4 eqrelrdvOLD.2 . . 3
5 eqrel 4814 . . 3
63, 4, 5mp2an 653 . 2
72, 6sylibr 203 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176  wal 1531   wceq 1633   wcel 1701  cop 3677   wrel 4731 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1537  ax-5 1548  ax-17 1607  ax-9 1645  ax-8 1666  ax-14 1705  ax-6 1720  ax-7 1725  ax-11 1732  ax-12 1897  ax-ext 2297  ax-sep 4178  ax-nul 4186  ax-pr 4251 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1533  df-nf 1536  df-sb 1640  df-clab 2303  df-cleq 2309  df-clel 2312  df-nfc 2441  df-ne 2481  df-v 2824  df-dif 3189  df-un 3191  df-in 3193  df-ss 3200  df-nul 3490  df-if 3600  df-sn 3680  df-pr 3681  df-op 3683  df-opab 4115  df-xp 4732  df-rel 4733
 Copyright terms: Public domain W3C validator