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Theorem opi2 4720
 Description: One of the two elements of an ordered pair. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 26-Apr-2015.) (Avoid depending on this detail.)
Hypotheses
Ref Expression
opi1.1
opi1.2
Assertion
Ref Expression
opi2

Proof of Theorem opi2
StepHypRef Expression
1 prex 4694 . . 3
21prid2 4139 . 2
3 opi1.1 . . 3
4 opi1.2 . . 3
53, 4dfop 4216 . 2
62, 5eleqtrri 2544 1
 Colors of variables: wff setvar class Syntax hints:  e.wcel 1818   cvv 3109  {csn 4029  {cpr 4031  <.cop 4035 This theorem is referenced by:  opeluu  4721  uniopel  4756  elvvuni  5065 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-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-v 3111  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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