Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  dfpr2 Unicode version

Theorem dfpr2 3560
 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 3551 . 2
2 elun 3226 . . . 4
3 elsn 3559 . . . . 5
4 elsn 3559 . . . . 5
53, 4orbi12i 509 . . . 4
62, 5bitri 242 . . 3
76abbi2i 2360 . 2
81, 7eqtri 2273 1
 Colors of variables: wff set class Syntax hints:   wo 359   wceq 1619   wcel 1621  cab 2239   cun 3076  csn 3544  cpr 3545 This theorem is referenced by:  elprg  3561  nfpr  3584  pwpw0  3663  pwsn  3721  pwsnALT  3722  zfpair  4106  grothprimlem  8335 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-v 2729  df-un 3083  df-sn 3550  df-pr 3551
 Copyright terms: Public domain W3C validator