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Theorem pwpr 4245
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 4193 . . . 4
2 vex 3112 . . . . . 6
32elpr 4047 . . . . 5
42elpr 4047 . . . . 5
53, 4orbi12i 521 . . . 4
61, 5bitr4i 252 . . 3
7 selpw 4019 . . 3
8 elun 3644 . . 3
96, 7, 83bitr4i 277 . 2
109eqriv 2453 1
Colors of variables: wff setvar class
Syntax hints:  \/wo 368  =wceq 1395  e.wcel 1818  u.cun 3473  C_wss 3475   c0 3784  ~Pcpw 4012  {csn 4029  {cpr 4031
This theorem is referenced by:  pwpwpw0  4247  ord3ex  4642  hash2pwpr  12519  pr2pwpr  12520  prsiga  28131
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-pw 4014  df-sn 4030  df-pr 4032
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