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Theorem opabn0 4783
 Description: Nonempty ordered pair class abstraction. (Contributed by NM, 10-Oct-2007.)
Assertion
Ref Expression
opabn0

Proof of Theorem opabn0
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 n0 3794 . 2
2 elopab 4760 . . . 4
32exbii 1667 . . 3
4 exrot3 1852 . . . 4
5 opex 4716 . . . . . . 7
65isseti 3115 . . . . . 6
7 19.41v 1771 . . . . . 6
86, 7mpbiran 918 . . . . 5
982exbii 1668 . . . 4
104, 9bitri 249 . . 3
113, 10bitri 249 . 2
121, 11bitri 249 1
 Colors of variables: wff setvar class Syntax hints:  <->wb 184  /\wa 369  =wceq 1395  E.wex 1612  e.wcel 1818  =/=wne 2652   c0 3784  <.cop 4035  {copab 4509 This theorem is referenced by:  csbopab  4784  dvdsrval  17294  thlle  18728  bcthlem5  21767  lgsquadlem3  23631 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-nul 4581  ax-pr 4691 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  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-ne 2654  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-opab 4511
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