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Theorem unopab 4284
 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 3608 . . 3
2 19.43 1615 . . . . 5
3 andi 838 . . . . . . . 8
43exbii 1592 . . . . . . 7
5 19.43 1615 . . . . . . 7
64, 5bitr2i 242 . . . . . 6
76exbii 1592 . . . . 5
82, 7bitr3i 243 . . . 4
98abbii 2548 . . 3
101, 9eqtri 2456 . 2
11 df-opab 4267 . . 3
12 df-opab 4267 . . 3
1311, 12uneq12i 3499 . 2
14 df-opab 4267 . 2
1510, 13, 143eqtr4i 2466 1
 Colors of variables: wff set class Syntax hints:   wo 358   wa 359  wex 1550   wceq 1652  cab 2422   cun 3318  cop 3817  copab 4265 This theorem is referenced by:  xpundi  4930  xpundir  4931  cnvun  5277  coundi  5371  coundir  5372  mptun  5575  opsrtoslem1  16544  lgsquadlem3  21140 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-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2958  df-un 3325  df-opab 4267
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