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Theorem preqr2g 3662
 Description: Reverse equality lemma for unordered pairs. If two unordered pairs have the same second element, the second elements are equal. Closed form of preqr2 3664. (Contributed by Jim Kingdon, 21-Sep-2018.)
Assertion
Ref Expression
preqr2g

Proof of Theorem preqr2g
StepHypRef Expression
1 prcom 3567 . . 3
2 prcom 3567 . . 3
31, 2eqeq12i 2129 . 2
4 preqr1g 3661 . 2
53, 4syl5bi 151 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wceq 1314   wcel 1463  cvv 2658  cpr 3496 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 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097 This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-v 2660  df-un 3043  df-sn 3501  df-pr 3502 This theorem is referenced by:  opth  4127
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