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Theorem elop 4132
 Description: An ordered pair has two elements. Exercise 3 of [TakeutiZaring] p. 15. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 26-Apr-2015.)
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 3695 . . 3
43eleq2i 2317 . 2
5 elop.1 . . 3
65elpr 3562 . 2
74, 6bitri 242 1
 Colors of variables: wff set class Syntax hints:   wb 178   wo 359   wceq 1619   wcel 1621  cvv 2727  csn 3544  cpr 3545  cop 3547 This theorem is referenced by:  relop  4741 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 941  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-v 2729  df-dif 3081  df-un 3083  df-in 3085  df-ss 3089  df-nul 3363  df-if 3471  df-sn 3550  df-pr 3551  df-op 3553
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