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Theorem dfpr2 4044
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 4032 . 2
2 elun 3644 . . . 4
3 elsn 4043 . . . . 5
4 elsn 4043 . . . . 5
53, 4orbi12i 521 . . . 4
62, 5bitri 249 . . 3
76abbi2i 2590 . 2
81, 7eqtri 2486 1
Colors of variables: wff setvar class
Syntax hints:  \/wo 368  =wceq 1395  e.wcel 1818  {cab 2442  u.cun 3473  {csn 4029  {cpr 4031
This theorem is referenced by:  elprg  4045  nfpr  4076  pwpw0  4178  pwsn  4243  pwsnALT  4244  zfpair  4689  grothprimlem  9232  nb3graprlem1  24451
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-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-un 3480  df-sn 4030  df-pr 4032
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