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Theorem unopab 4016
 Description: Union of two ordered pair class abstractions. (Contributed by NM, 30-Sep-2002.)
Assertion
Ref Expression
unopab

Proof of Theorem unopab
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 unab 3349 . . 3
2 19.43 1608 . . . . 5
3 andi 808 . . . . . . . 8
43exbii 1585 . . . . . . 7
5 19.43 1608 . . . . . . 7
64, 5bitr2i 184 . . . . . 6
76exbii 1585 . . . . 5
82, 7bitr3i 185 . . . 4
98abbii 2256 . . 3
101, 9eqtri 2161 . 2
11 df-opab 3999 . . 3
12 df-opab 3999 . . 3
1311, 12uneq12i 3234 . 2
14 df-opab 3999 . 2
1510, 13, 143eqtr4i 2171 1
 Colors of variables: wff set class Syntax hints:   wa 103   wo 698   wceq 1332  wex 1469  cab 2126   cun 3075  cop 3536  copab 3997 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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2692  df-un 3081  df-opab 3999 This theorem is referenced by:  xpundi  4605  xpundir  4606  cnvun  4954  coundi  5050  coundir  5051  mptun  5264
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