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Theorem euop2 4752
 Description: Transfer existential uniqueness to second member of an ordered pair. (Contributed by NM, 10-Apr-2004.)
Hypothesis
Ref Expression
euop2.1
Assertion
Ref Expression
euop2
Distinct variable groups:   ,   ,   ,

Proof of Theorem euop2
StepHypRef Expression
1 opex 4716 . 2
2 euop2.1 . . 3
32moop2 4747 . 2
41, 3euxfr2 3284 1
 Colors of variables: wff setvar class Syntax hints:  <->wb 184  /\wa 369  =wceq 1395  E.wex 1612  e.wcel 1818  E!weu 2282   cvv 3109  <.cop 4035 This theorem is referenced by:  dfac5lem1  8525 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-rab 2816  df-v 3111  df-sbc 3328  df-csb 3435  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036
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