Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  dfpr2 Unicode version

Theorem dfpr2 3394
 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 3382 . 2
2 elun 3084 . . . 4
3 velsn 3392 . . . . 5
4 velsn 3392 . . . . 5
53, 4orbi12i 681 . . . 4
62, 5bitri 173 . . 3
76abbi2i 2152 . 2
81, 7eqtri 2060 1
 Colors of variables: wff set class Syntax hints:   wo 629   wceq 1243   wcel 1393  cab 2026   cun 2915  csn 3375  cpr 3376 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-sn 3381  df-pr 3382 This theorem is referenced by:  elprg  3395  nfpr  3420  pwsnss  3574
 Copyright terms: Public domain W3C validator