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Theorem pwpr 4011
 Description: The power set of an unordered pair. (Contributed by NM, 1-May-2009.)
Assertion
Ref Expression
pwpr

Proof of Theorem pwpr
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sspr 3962 . . . 4
2 vex 2959 . . . . . 6
32elpr 3832 . . . . 5
42elpr 3832 . . . . 5
53, 4orbi12i 508 . . . 4
61, 5bitr4i 244 . . 3
72elpw 3805 . . 3
8 elun 3488 . . 3
96, 7, 83bitr4i 269 . 2
109eqriv 2433 1
 Colors of variables: wff set class Syntax hints:   wo 358   wceq 1652   wcel 1725   cun 3318   wss 3320  c0 3628  cpw 3799  csn 3814  cpr 3815 This theorem is referenced by:  pwpwpw0  4013  ord3ex  4389  prsiga  24514 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-pw 3801  df-sn 3820  df-pr 3821
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