Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  kmlem5 Structured version   Unicode version

Theorem kmlem5 8566
 Description: Lemma for 5-quantifier AC of Kurt Maes, Th. 4, part of 3 => 4. (Contributed by NM, 25-Mar-2004.)
Assertion
Ref Expression
kmlem5
Distinct variable group:   ,,

Proof of Theorem kmlem5
StepHypRef Expression
1 difss 3570 . . . 4
2 sslin 3665 . . . 4
31, 2ax-mp 5 . . 3
4 kmlem4 8565 . . 3
53, 4syl5sseq 3490 . 2
6 ss0b 3769 . 2
75, 6sylib 196 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 367   wceq 1405   wne 2598   cdif 3411   cin 3413   wss 3414  c0 3738  csn 3972  cuni 4191 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380 This theorem depends on definitions:  df-bi 185  df-an 369  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-ne 2600  df-ral 2759  df-v 3061  df-dif 3417  df-in 3421  df-ss 3428  df-nul 3739  df-sn 3973  df-uni 4192 This theorem is referenced by:  kmlem9  8570
 Copyright terms: Public domain W3C validator