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Theorem uniop 4269
 Description: The union of an ordered pair. Theorem 65 of [Suppes] p. 39. (Contributed by NM, 17-Aug-2004.) (Revised by Mario Carneiro, 26-Apr-2015.)
Hypotheses
Ref Expression
opthw.1
opthw.2
Assertion
Ref Expression
uniop

Proof of Theorem uniop
StepHypRef Expression
1 opthw.1 . . . 4
2 opthw.2 . . . 4
31, 2dfop 3795 . . 3
43unieqi 3837 . 2
5 snex 4216 . . 3
6 prex 4217 . . 3
75, 6unipr 3841 . 2
8 snsspr1 3764 . . 3
9 ssequn1 3345 . . 3
108, 9mpbi 199 . 2
114, 7, 103eqtri 2307 1
 Colors of variables: wff set class Syntax hints:   wceq 1623   wcel 1684  cvv 2788   cun 3150   wss 3152  csn 3640  cpr 3641  cop 3643  cuni 3827 This theorem is referenced by:  uniopel  4270  elvvuni  4750  dmrnssfld  4938  dffv2  5592  rankxplim  7549 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-rex 2549  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-uni 3828
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