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Theorem dmopabss 5081
 Description: Upper bound for the domain of a restricted class of ordered pairs. (Contributed by NM, 31-Jan-2004.)
Assertion
Ref Expression
dmopabss
Distinct variable group:   ,,
Allowed substitution hints:   (,)

Proof of Theorem dmopabss
StepHypRef Expression
1 dmopab 5080 . 2
2 19.42v 1928 . . . 4
32abbii 2548 . . 3
4 ssab2 3427 . . 3
53, 4eqsstri 3378 . 2
61, 5eqsstri 3378 1
 Colors of variables: wff set class Syntax hints:   wa 359  wex 1550   wcel 1725  cab 2422   wss 3320  copab 4265   cdm 4878 This theorem is referenced by:  fvopab4ndm  5825  opabex  5964  dmadjss  23390  abrexdomjm  23988  abrexdom  26432 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-br 4213  df-opab 4267  df-dm 4888
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