MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  kmlem15 Unicode version

Theorem kmlem15 8565
Description: Lemma for 5-quantifier AC of Kurt Maes, Th. 4, part of 5 <=> 4. (Contributed by NM, 4-Apr-2004.)
Hypotheses
Ref Expression
kmlem14.1
kmlem14.2
kmlem14.3
Assertion
Ref Expression
kmlem15
Distinct variable groups:   , , , ,   ,

Proof of Theorem kmlem15
StepHypRef Expression
1 kmlem14.3 . . . 4
2 nfv 1707 . . . . . . 7
32eu1 2327 . . . . . 6
4 elin 3686 . . . . . . . . 9
5 clelsb3 2578 . . . . . . . . . . . 12
6 elin 3686 . . . . . . . . . . . 12
75, 6bitri 249 . . . . . . . . . . 11
8 equcom 1794 . . . . . . . . . . 11
97, 8imbi12i 326 . . . . . . . . . 10
109albii 1640 . . . . . . . . 9
114, 10anbi12i 697 . . . . . . . 8
12 19.28v 1767 . . . . . . . 8
1311, 12bitr4i 252 . . . . . . 7
1413exbii 1667 . . . . . 6
153, 14bitri 249 . . . . 5
1615ralbii 2888 . . . 4
17 df-ral 2812 . . . . 5
18 kmlem14.2 . . . . . . . . . 10
1918albii 1640 . . . . . . . . 9
20 19.21v 1729 . . . . . . . . 9
2119, 20bitri 249 . . . . . . . 8
2221exbii 1667 . . . . . . 7
23 19.37v 1768 . . . . . . 7
2422, 23bitri 249 . . . . . 6
2524albii 1640 . . . . 5
2617, 25bitr4i 252 . . . 4
271, 16, 263bitri 271 . . 3
2827anbi2i 694 . 2
29 19.28v 1767 . 2
30 19.28v 1767 . . . . 5
3130exbii 1667 . . . 4
32 19.42v 1775 . . . 4
3331, 32bitr2i 250 . . 3
3433albii 1640 . 2
3528, 29, 343bitr2i 273 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  E.wex 1612  [wsb 1739  e.wcel 1818  E!weu 2282  =/=wne 2652  A.wral 2807  i^icin 3474
This theorem is referenced by:  kmlem16  8566
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-eu 2286  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-v 3111  df-in 3482
  Copyright terms: Public domain W3C validator