Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  zfpair2 Unicode version

Theorem zfpair2 4132
 Description: Derive the abbreviated version of the Axiom of Pairing from ax-pr 4131. (Contributed by NM, 14-Nov-2006.)
Assertion
Ref Expression
zfpair2

Proof of Theorem zfpair2
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 ax-pr 4131 . . . 4
21bm1.3ii 4049 . . 3
3 dfcleq 2133 . . . . 5
4 vex 2689 . . . . . . . 8
54elpr 3548 . . . . . . 7
65bibi2i 226 . . . . . 6
76albii 1446 . . . . 5
83, 7bitri 183 . . . 4
98exbii 1584 . . 3
102, 9mpbir 145 . 2
1110issetri 2695 1
 Colors of variables: wff set class Syntax hints:   wb 104   wo 697  wal 1329   wceq 1331  wex 1468   wcel 1480  cvv 2686  cpr 3528 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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-14 1492  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121  ax-sep 4046  ax-pr 4131 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-un 3075  df-sn 3533  df-pr 3534 This theorem is referenced by:  prexg  4133  onintexmid  4487  funopg  5157
 Copyright terms: Public domain W3C validator