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Theorem dfpr2 3822
 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 3813 . 2
2 elun 3480 . . . 4
3 elsn 3821 . . . . 5
4 elsn 3821 . . . . 5
53, 4orbi12i 508 . . . 4
62, 5bitri 241 . . 3
76abbi2i 2546 . 2
81, 7eqtri 2455 1
 Colors of variables: wff set class Syntax hints:   wo 358   wceq 1652   wcel 1725  cab 2421   cun 3310  csn 3806  cpr 3807 This theorem is referenced by:  elprg  3823  nfpr  3847  pwpw0  3938  pwsn  4001  pwsnALT  4002  zfpair  4393  grothprimlem  8700  nb3graprlem1  21452 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 2416 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 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-un 3317  df-sn 3812  df-pr 3813
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