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Theorem uniop 4693
 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 4158 . . 3
43unieqi 4200 . 2
5 snex 4632 . . 3
6 prex 4633 . . 3
75, 6unipr 4204 . 2
8 snsspr1 4121 . . 3
9 ssequn1 3613 . . 3
108, 9mpbi 208 . 2
114, 7, 103eqtri 2435 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1405   wcel 1842  cvv 3059   cun 3412   wss 3414  csn 3972  cpr 3974  cop 3978  cuni 4191 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-9 1846  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380  ax-sep 4517  ax-nul 4525  ax-pr 4630 This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3an 976  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-ne 2600  df-rex 2760  df-v 3061  df-dif 3417  df-un 3419  df-in 3421  df-ss 3428  df-nul 3739  df-if 3886  df-sn 3973  df-pr 3975  df-op 3979  df-uni 4192 This theorem is referenced by:  uniopel  4694  elvvuni  4884  dmrnssfld  5082  dffv2  5922  rankxplim  8329
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