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Theorem elop 4718
Description: An ordered pair has two elements. Exercise 3 of [TakeutiZaring] p. 15. (Contributed by NM, 15-Jul-1993.) (Revised by Mario Carneiro, 26-Apr-2015.) (Avoid depending on this detail.)
Hypotheses
Ref Expression
elop.1
elop.2
elop.3
Assertion
Ref Expression
elop

Proof of Theorem elop
StepHypRef Expression
1 elop.2 . . . 4
2 elop.3 . . . 4
31, 2dfop 4216 . . 3
43eleq2i 2535 . 2
5 elop.1 . . 3
65elpr 4047 . 2
74, 6bitri 249 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  \/wo 368  =wceq 1395  e.wcel 1818   cvv 3109  {csn 4029  {cpr 4031  <.cop 4035
This theorem is referenced by:  relop  5158
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-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
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-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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