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Theorem preqr2 3965
 Description: Reverse equality lemma for unordered pairs. If two unordered pairs have the same first element, the second elements are equal. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
preqr2.1
preqr2.2
Assertion
Ref Expression
preqr2

Proof of Theorem preqr2
StepHypRef Expression
1 prcom 3874 . . 3
2 prcom 3874 . . 3
31, 2eqeq12i 2448 . 2
4 preqr2.1 . . 3
5 preqr2.2 . . 3
64, 5preqr1 3964 . 2
73, 6sylbi 188 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652   wcel 1725  cvv 2948  cpr 3807 This theorem is referenced by:  preq12b  3966  opth  4427  opthreg  7565  usgra2edg  21394  usgraedgreu  21399  nbgraf1olem5  21447  altopthsn  25798 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-un 3317  df-sn 3812  df-pr 3813
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