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Theorem unopab 3836
 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 3204 . . 3
2 19.43 1519 . . . . 5
3 andi 731 . . . . . . . 8
43exbii 1496 . . . . . . 7
5 19.43 1519 . . . . . . 7
64, 5bitr2i 174 . . . . . 6
76exbii 1496 . . . . 5
82, 7bitr3i 175 . . . 4
98abbii 2153 . . 3
101, 9eqtri 2060 . 2
11 df-opab 3819 . . 3
12 df-opab 3819 . . 3
1311, 12uneq12i 3095 . 2
14 df-opab 3819 . 2
1510, 13, 143eqtr4i 2070 1
 Colors of variables: wff set class Syntax hints:   wa 97   wo 629   wceq 1243  wex 1381  cab 2026   cun 2915  cop 3378  copab 3817 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-opab 3819 This theorem is referenced by:  xpundi  4396  xpundir  4397  cnvun  4729  coundi  4822  coundir  4823  mptun  5029
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