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Theorem dfpr2 3749
 Description: Alternate definition of unordered pair. Definition 5.1 of [TakeutiZaring] p. 15. (Contributed by NM, 24-Apr-1994.)
Assertion
Ref Expression
dfpr2
Distinct variable groups:   ,   ,

Proof of Theorem dfpr2
StepHypRef Expression
1 df-pr 3742 . 2
2 elun 3220 . . . 4
3 elsn 3748 . . . . 5
4 elsn 3748 . . . . 5
53, 4orbi12i 507 . . . 4
62, 5bitri 240 . . 3
76abbi2i 2464 . 2
81, 7eqtri 2373 1
 Colors of variables: wff setvar class Syntax hints:   wo 357   wceq 1642   wcel 1710  cab 2339   cun 3207  csn 3737  cpr 3738 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-un 3214  df-sn 3741  df-pr 3742 This theorem is referenced by:  elprg  3750  nfpr  3773  pwpw0  3855  pwsn  3881  pwsnALT  3882
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