New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  unopab Unicode version

Theorem unopab 4638
 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 3521 . . 3
2 19.43 1605 . . . . 5
3 andi 837 . . . . . . . 8
43exbii 1582 . . . . . . 7
5 19.43 1605 . . . . . . 7
64, 5bitr2i 241 . . . . . 6
76exbii 1582 . . . . 5
82, 7bitr3i 242 . . . 4
98abbii 2465 . . 3
101, 9eqtri 2373 . 2
11 df-opab 4623 . . 3
12 df-opab 4623 . . 3
1311, 12uneq12i 3416 . 2
14 df-opab 4623 . 2
1510, 13, 143eqtr4i 2383 1
 Colors of variables: wff setvar class Syntax hints:   wo 357   wa 358  wex 1541   wceq 1642  cab 2339   cun 3207  cop 4561  copab 4622 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-un 3214  df-opab 4623 This theorem is referenced by:  xpundi  4832  xpundir  4833  cnvun  5033  coundi  5082  coundir  5083
 Copyright terms: Public domain W3C validator