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Theorem dfpr2 3514
 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 3502 . 2
2 elun 3185 . . . 4
3 velsn 3512 . . . . 5
4 velsn 3512 . . . . 5
53, 4orbi12i 736 . . . 4
62, 5bitri 183 . . 3
76abbi2i 2230 . 2
81, 7eqtri 2136 1
 Colors of variables: wff set class Syntax hints:   wo 680   wceq 1314   wcel 1463  cab 2101   cun 3037  csn 3495  cpr 3496 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097 This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-v 2660  df-un 3043  df-sn 3501  df-pr 3502 This theorem is referenced by:  elprg  3515  nfpr  3541  pwsnss  3698  minmax  10952  xrminmax  10985
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