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Theorem unopab 4527
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 3764 . . 3
2 19.43 1693 . . . . 5
3 andi 867 . . . . . . . 8
43exbii 1667 . . . . . . 7
5 19.43 1693 . . . . . . 7
64, 5bitr2i 250 . . . . . 6
76exbii 1667 . . . . 5
82, 7bitr3i 251 . . . 4
98abbii 2591 . . 3
101, 9eqtri 2486 . 2
11 df-opab 4511 . . 3
12 df-opab 4511 . . 3
1311, 12uneq12i 3655 . 2
14 df-opab 4511 . 2
1510, 13, 143eqtr4i 2496 1
Colors of variables: wff setvar class
Syntax hints:  \/wo 368  /\wa 369  =wceq 1395  E.wex 1612  {cab 2442  u.cun 3473  <.cop 4035  {copab 4509
This theorem is referenced by:  xpundi  5057  xpundir  5058  cnvun  5416  coundi  5513  coundir  5514  mptun  5717  opsrtoslem1  18148  lgsquadlem3  23631
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-un 3480  df-opab 4511
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