MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  kmlem16 Unicode version

Theorem kmlem16 8566
Description: Lemma for 5-quantifier AC of Kurt Maes, Th. 4 5 <=> 4. (Contributed by NM, 4-Apr-2004.)
Hypotheses
Ref Expression
kmlem14.1
kmlem14.2
kmlem14.3
Assertion
Ref Expression
kmlem16
Distinct variable groups:   , , , , ,   ,

Proof of Theorem kmlem16
StepHypRef Expression
1 kmlem14.1 . . . 4
2 kmlem14.2 . . . 4
3 kmlem14.3 . . . 4
41, 2, 3kmlem14 8564 . . 3
51, 2, 3kmlem15 8565 . . . 4
65exbii 1667 . . 3
74, 6orbi12i 521 . 2
8 19.43 1693 . 2
9 pm3.24 882 . . . . . 6
10 simpl 457 . . . . . . . . 9
1110sps 1865 . . . . . . . 8
1211exlimivv 1723 . . . . . . 7
13 simpl 457 . . . . . . . . 9
1413sps 1865 . . . . . . . 8
1514exlimivv 1723 . . . . . . 7
1612, 15anim12i 566 . . . . . 6
179, 16mto 176 . . . . 5
18 19.33b 1696 . . . . 5
1917, 18ax-mp 5 . . . 4
2010exlimiv 1722 . . . . . . . . . 10
2113exlimiv 1722 . . . . . . . . . 10
2220, 21anim12i 566 . . . . . . . . 9
239, 22mto 176 . . . . . . . 8
24 19.33b 1696 . . . . . . . 8
2523, 24ax-mp 5 . . . . . . 7
2625exbii 1667 . . . . . 6
27 19.43 1693 . . . . . 6
2826, 27bitr2i 250 . . . . 5
2928albii 1640 . . . 4
3019, 29bitr3i 251 . . 3
3130exbii 1667 . 2
327, 8, 313bitr2i 273 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  <->wb 184  \/wo 368  /\wa 369  A.wal 1393  E.wex 1612  e.wcel 1818  E!weu 2282  =/=wne 2652  A.wral 2807  E.wrex 2808  i^icin 3474
This theorem is referenced by:  dfackm  8567
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-ne 2654  df-ral 2812  df-rex 2813  df-v 3111  df-in 3482
  Copyright terms: Public domain W3C validator