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Theorem uniop 4227
 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 3755 . . 3
43unieqi 3797 . 2
5 snex 4174 . . 3
6 prex 4175 . . 3
75, 6unipr 3801 . 2
8 snsspr1 3724 . . 3
9 ssequn1 3306 . . 3
108, 9mpbi 201 . 2
114, 7, 103eqtri 2280 1
 Colors of variables: wff set class Syntax hints:   wceq 1619   wcel 1621  cvv 2757   cun 3111   wss 3113  csn 3600  cpr 3601  cop 3603  cuni 3787 This theorem is referenced by:  uniopel  4228  elvvuni  4724  dmrnssfld  4912  dffv2  5512  rankxplim  7503 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 1927  ax-ext 2237  ax-sep 4101  ax-nul 4109  ax-pr 4172 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 1884  df-clab 2243  df-cleq 2249  df-clel 2252  df-nfc 2381  df-ne 2421  df-rex 2522  df-v 2759  df-dif 3116  df-un 3118  df-in 3120  df-ss 3127  df-nul 3417  df-if 3526  df-sn 3606  df-pr 3607  df-op 3609  df-uni 3788
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