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Theorem preqr2 3696
 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 3599 . . 3
2 prcom 3599 . . 3
31, 2eqeq12i 2153 . 2
4 preqr2.1 . . 3
5 preqr2.2 . . 3
64, 5preqr1 3695 . 2
73, 6sylbi 120 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1331   wcel 1480  cvv 2686  cpr 3528 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-un 3075  df-sn 3533  df-pr 3534 This theorem is referenced by:  preq12b  3697  opth  4159  opthreg  4471
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