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Theorem opabn0 4488
 Description: Non-empty 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 3639 . 2
2 elopab 4465 . . . 4
32exbii 1593 . . 3
4 exrot3 1760 . . . 4
5 opex 4430 . . . . . . 7
65isseti 2964 . . . . . 6
7 19.41v 1925 . . . . . 6
86, 7mpbiran 886 . . . . 5
982exbii 1594 . . . 4
104, 9bitri 242 . . 3
113, 10bitri 242 . 2
121, 11bitri 242 1
 Colors of variables: wff set class Syntax hints:   wb 178   wa 360  wex 1551   wceq 1653   wcel 1726   wne 2601  c0 3630  cop 3819  copab 4268 This theorem is referenced by:  dvdsrval  15755  thlle  16929  bcthlem5  19286  lgsquadlem3  21145 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4333  ax-nul 4341  ax-pr 4406 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-opab 4270
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