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Theorem opthg 4139
 Description: Ordered pair theorem. and are not required to be sets under our specific ordered pair definition. (Contributed by NM, 14-Oct-2005.) (Revised by Mario Carneiro, 26-Apr-2015.)
Assertion
Ref Expression
opthg

Proof of Theorem opthg
StepHypRef Expression
1 opeq1 3696 . . . 4
21eqeq1d 2261 . . 3
3 eqeq1 2259 . . . 4
43anbi1d 688 . . 3
52, 4bibi12d 314 . 2
6 opeq2 3697 . . . 4
76eqeq1d 2261 . . 3
8 eqeq1 2259 . . . 4
98anbi2d 687 . . 3
107, 9bibi12d 314 . 2
11 vex 2730 . . 3
12 vex 2730 . . 3
1311, 12opth 4138 . 2
145, 10, 13vtocl2g 2785 1
 Colors of variables: wff set class Syntax hints:   wi 6   wb 178   wa 360   wceq 1619   wcel 1621  cop 3547 This theorem is referenced by:  opthg2  4140  oteqex  4152  s111  11325  frgpnabllem1  14996  frgpnabllem2  14997  dvheveccl  29991 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-14 1626  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234  ax-sep 4038  ax-nul 4046  ax-pr 4108 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-ne 2414  df-rab 2516  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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