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Theorem zfpair2 4692
Description: Derive the abbreviated version of the Axiom of Pairing from ax-pr 4691. See zfpair 4689 for its derivation from the other axioms. (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 4691 . . . 4
21bm1.3ii 4576 . . 3
3 dfcleq 2450 . . . . 5
4 vex 3112 . . . . . . . 8
54elpr 4047 . . . . . . 7
65bibi2i 313 . . . . . 6
76albii 1640 . . . . 5
83, 7bitri 249 . . . 4
98exbii 1667 . . 3
102, 9mpbir 209 . 2
1110issetri 3116 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  \/wo 368  A.wal 1393  =wceq 1395  E.wex 1612  e.wcel 1818   cvv 3109  {cpr 4031
This theorem is referenced by:  snex  4693  prex  4694  pwssun  4791  xpsspwOLD  5122  funopg  5625  fiint  7817  brdom7disj  8930  brdom6disj  8931  wlkntrllem1  24561  frisusgranb  24997  2pthfrgrarn  25009
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-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-pr 4691
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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